How much of a temperature rise are we talking about? Keep in mind most of the off flavors in beer are a result of how the yeast were treated in the lag and growth phases, both of which you're probably well past.
I've got one of those too but never thought about using it as a mash tun....hummm. I did use it last winter though along with some towels, a heating pad, and a ranco temp controller to keep a glass carboy at ale fermenting temps. Worked great for that.
I know I'm a little late to the party but I've also experienced the seemingly forever ramp up time of 2206. I had a pack of 2206 that had been in the fridge for about 5 months. Smacked it and after two days there was NO swelling. I figured it was dead but just left it on the counter...