Thermistors, fans? I suspect that the modded chargers blow up because of marginal derating rather than temperature, you are probably wasting time with that stuff.
Do you have a scope? Post the waveform on the secondary winding, before the rectifier, and report voltage on the primary capacitor (don't blow it up, don't kill yourself, yada yada). This will help estimate turns ratio of the transformer.
Is the secondary rectifier that STPS20150C diode that you mentioned earlier? What's the maximum secondary output voltage?
The primary switch may need an upgrade, because it sees rectified mains plus secondary voltage multiplied by turns ratio plus inductive kickback from the transformer's leakage inductance.
I'm still not sure what to think about the circuit in the center, and yes, I too think that box is a transformer. Not sure what the whole thing is doing, maybe an auxilliary PSU for some secondary circuits?
edit
There is likely a high value (1Meg or so) resistor which pulls UC3845's VCC up before the converter starts working and produces its own supply voltage. This may need checking for proper power and voltage rating. Or just desolder one end and add an identical resistor in series.