i have a 96 taco with a 2.7 and it does the same thing. The circut opening relay causes this. It controls power to your fuel pump and when it gets to hot it can stick and send no power to your fuel pump, toyota mounted the relay on a heater duct just to the left of your steering column under the dash. In the winter my truck never does this but in the summer it wont fire after driving it quite frequently. The only reason i havent replaced the relay is because it was $90 at my local dealer.
Honestly, this sounds suspect.
A couple of things.
First, the COR is mounted on the bottom of the fuse panel.
Second, even if Toyota mounted the relay ON a heater duct (which they never would), the heat generated on the OUTSIDE of a duct would never be enough to cause a relay to not function. Even if it was mounted IN the duct, it wouldn't either by the way.
Third, if it was heat that was causing it to stick the it would stick closed since it was warm when it "stuck" since the motor was running. this would cause it not to turn OFF the pump rather than causing it to not turn on.
Here is what the COR looks like. Again, located at the bottom of the fuse panel.
I would grab a test light or meter and check your voltage at the small trigger wire on the starter when it WONT start and see if you have voltage there.
If not, then trace that back and find where the interrupt is. If you do have voltage, then you have a bad starter (most likely)
