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...   
