I disagree with the premise that thicker pipe chamber walls necessarily yield a "cooler" smoke. Smoking quality is determined by a system of things that include tobacco chemistry, tobacco moisture, the smoker's mouth chemistry and puffing style, chamber depth and diameter, packing style, environmental factors like ambient temperature and humidity, and certainly other factors. If by "cooler" we are to understand that the overall smoking experience is pleasant, then the chamber wall thickness has little to do with it.
For example, I enjoy a diminutive Peterson Belgique briar pipe with a small chamber and very thin chamber walls. One would think that it's a nightmare to smoke, but that is not the case. It's very enjoyable with the tobaccos that I like to smoke in it, such as Peterson's De Luxe Navy Rolls. Also, exterior temperature of the bowl is warm, and never hot.
If you're having trouble with a particular tobacco, consider switching to a different family of tobaccos. For example, from tobacco based on red Virginia to tobacco based on burley. Or from heavily sweetened aromatics to Englishes.
My personal journey to the perfect smoke did not depend on better equipment, it depended on better technique, and on tobaccos better suited to me as an individual. I had a few decent mid-range ($100-$150) briars by good manufacturers (Peterson and Savinelli), in common designs (billiards initially). That was good enough.
Today I own larger bowled pipes with thicker chamber walls and I like them, but I still favor the standard sizes in classic designs that are most familiar to pipe smokers.
What works for me is to find a tobacco that seems to have potential, and then dial in my technique to smoke it well. I also am not reluctant to discard tobaccos I don't like. Some are kept in a probationary status to age for a while for a later trial, but I usually end up discarding them too.