a cheap, slow, lame solution ... :
Make a solar convection oven.
he hit 380. I'd think you would want about 200F to heat cycle a tire make it just big enough to fit 1 tire. sure not perfectly ideal but it could easily be done...
you could literally just line a cardboard box with tin foil . put saran wrap over the top and the 4 "tops" could also be lined for a bit of a reflector. probably cost you $1 (if you already have a box) i have a box large enough for a tire if you need one, or are actually interested in my horrible idea...