I keep burning my tongue and the roof of my mouth

Slow down. You're pulling smoke and steam into your mouth, so if you draw in too much, too fast, it's going to hurt. Still happens to me occasionally if I'm not paying enough attention.

Andy,
Let it heal. Then slow down... a lot! Don't let the bowl get hot ever. If it begins to, let it cool before relighting. Take small sips and do not draw the smoke toward back of tongue or roof of mouth. You can still exhale through nose but don't draw the smoke (heat) to back of mouth as the roof of the mouth is more tender there.

+1 on all of the above.
I am still in the "getting my technique down" phase, but a few things I've done recently based on forum advice include letting the tobacco dry a little more than it seemed like I should, and not packing so tightly. These have both helped in not burning my tongue/roof of mouth (so much)--and also getting more flavor out of my smokes-- since more moisture in the tobacco + heat = steam = burn.

Fortunately the mouth heals remarkably quick. As others have stated it sounds like you need to slow down on the cadence. All of us have gone through it but there's no need to torture yourself. Just give it a little time, sip that pipe when you do re-start and if you feel the bite coming, slow down some more.

I kept thinking that I was smoking slow enough, but had the same issues. I still have to tell myself to slow down even more, just letting the smoke come into my mouth as I breath through my nose.
I used to keep aloe juice that you can get at the pharmacy to drink when I was trying a lot of different blends, thinking it was the tobacco's fault. It helped, and so does Biotene. This will speed up recovery to help you keep scorching it again, ha ha.
I think that sometimes the moment hits me, flavors taste so good when just letting it smolder slowly in the bowl, and I get excited and start drawing more on the pipe. Then I have to keep telling myself to slow down again.

+1 on what others have said. I find that "sipping" rather than "puffing" is a big help. Not only does it help with preventing tongue bite but it also allows you to better savor the flavor of the tobacco blend as well. When the tobacco begins to burn too hot then it also affects the flavor in a negative way. If the bowl starts to get hot to the touch then that's a good sign that you're drawing too much and you need to let it cool down and slow down on your intake. Not only does constantly getting the bowl hot risk tongue bite but it's also not good for your pipe either and can run greater risk of eventually causing a burnout. I usually pack my tobacco somewhat loose, often initially lightly tapping it with my pinky finger, and this seems to help with an easier draw so that I'm not having to work to draw enough through the stem to keep the pipe lit. Just keep practicing and you'll eventually get your technique down to pat.

The advise given by our experienced pipers has helped my work through this issue. Dry the tobacco first so steam won't be a problem, 8 to 12 seconds in the microwave when you are in a hurry will help. Slow down, and from Kashmir try clenching, it helps in maintaing a rythem and slow pace. Good luck with your tounge transplant.

Are you a clencher? I am, and it tends to be more of a curse than a blessing. With it just hanging there it's easy to just take one pull after another. I counterbalance it by trying to force myself to take the pipe out of my mouth here and there. I swear, these days I have a callous where the bit meets my tongue.

I tend to be a puffer and prefer aros so I used to have a real issue with tongue bite. Now I use filtered pipes for my wet aros and have added Biotene to my bed time ritual. Biotene does great things for your mouth as far as helping it stay hydrated and speeds the healing time of tongue burn. Filtered pipes are great as far as they have not affected my enjoyment of aros while working as a barrier to hot steam and juice.

I don't necessarily agree with the advice to pack looser, not without knowing how tightly Andy is packing now. Packing too loose is just as bad, maybe even worse, than packing too tight. A pipe too loosely packed will smoke very hot, especially if you're also drying your tobacco out. Dry tobacco loosely packed is a surefire recipe for hot smoke and tongue burn.
The firmness of the pack is determined by the cut of the tobacco and its moisture content. Andy hasn't given us enough information for us to say definitively that he's packing too tightly.
Slowing down is always great advice. Looking at videos on YouTube, it's apparent to me that a lot of pipe smokers have terrible technique. There shouldn't be huge clouds of smoke billowing from your mouth and pipe constantly. Properly smoked, a pipe will always be on the verge of going out. The idea is to smoke at the lowest possible temperature that maintains combustion. The tobacco will taste A LOT BETTER when you do this.
Just my humble opinions of course. If someone enjoys puffing away like a freight train and lighting their pipe with a blowtorch then who am I to piss against the wind?

Yes, as has been said many times above, slow down. Then slow down more, and then more.

I'm not an expert by any means (I am beginner ) but...

Here are few tips as I went trough that pain few weeks/months ago... take a few days rest until your tongue heals then:
1) slowdown, and take smaller sips

2) dry your tobacco (maybe it's too wet)

3) pack your pipe right (Frank's method works for me the best, swirl method is also a good one but I think it really depends on the tobacco (how loose it is cut etc..))

4) tobacco that you are smoking might not go down well on your tongue... in other words try to change tobacco (manufactures, types ...)

5) drink some good grog with ye pipe (lemonade (LOL) or something sour works best for me)) , eat well and don't be too tiered or hungry when you are smoking it (sounds stupid and general but it really improves your enjoyment)
These are all common advice you will find online and it should help with tongue bite
now here is one more tip, that I realized after burning my tongue several times...

very important is the moment when you burn your tongue and (for me) I realized that sometimes when I'm lighting my pipe I either puff too hard (as I'm mostly concentrated on a flame and tobacco) or that I put my matches or lighter too close to a bowl.. so try to keep it as far as you can as when you take a puff you will suck a flame into a bowl
And in the end it all gets easier and better with time... your tolerance for tongue bite becomes higher ye scurvy dog
Arrrrrrrrrrr!

Well, stop it.

First time I smoked, I burnt my mouth a lot. What really helped me was the Frank Method of packing... there is a nice video from pipesmagazine.com in youtube!
https://www.youtube.com/watch?v=XrgzFVmurUk
Try that!

Tongue bite is a pain. I mainly smoke in humid countries and, as I am not always able to smoke whenever I want at home, would find myself racing through a couple of bowls as soon as the opportunity would arise, burning my tongue horribly.
I was on the verge of giving up until a work trip to Germany when my pipe tobacco dried out nicely in my hotel room and I had the time that evening to smoke slowly and peacefully.
No tongue bite.
Since then I've made the effort to dry my tobacco more than I think it should need to be. Also, when time or opportunity are not to hand, I smoke a stronger blend slowly, as opposed to a milder blend quickly.

your tolerance for tongue bite becomes higher

Click to expand...

Hahaha, thats my method