I agree with everyone else's suggested first step of bee's wax and smoking a few bowls. If that fails however, my preferred method is to use a heat gun and machinists scribe. A decent hobbyists heat gun can be had at a relatively small price from most hobby stores, or you may be able to substitute your wife's hair dryer on the hottest s setting. I don't like the idea of using an open flame, too easy to damage the stem in my opinion. For the scribe just about any auto parts store, farm store or home improvement center should have something suitable, the key is a tapered shank.
Remove the stem and heart the tenon with the heat gun until it begins to soften. Once the tenon is malleable gently insert the scribe into the airway using a twisting motion. Take care not to be too aggressive as it is possible to split the tenon if the scribe's diameter is too large. Let the tenon cool slightly and test fit. If it is still too loose rinse and repeat. If the fit is too snug reheat the tenon and carefully insert it into the mortise to reduce the diameter for a perfect fit.
Best of luck, hope this helps!