My early 2009 17" mbp won't start after it has cooled down

This started last winter

The same happens if the computer is asleep, I will come back to it, it a key to wake it up, the screen turns on a split second and it turns off, then pressing the power button does nothing

I have now replaced the battery, but still have the same problem

The only way to turn it back on is to physically heat it slowly for about 10 minutes (on a wall heater, or on an electric stove, so the top case feels warm to the touch, then do an SMC reset (holding shift-control-opt and the power button 10 sec) then pressing the power button again. Sometimes it boots up half way and shuts down, but pressing the power button again (and or another smc reset I forgot) and it will complete the boot, and be fine

Have you guys seen this elsewhere?

Thanks

Ok thanks for your help, I should add that I replaced the battery because the original was swollen up big,and not leaking if it helps