If the TM has ran normally for some time now beings ran as you just did with never any problems, nothing has just been changed/modified such as new wiring just added etc and it never had burning/hot wires before and has ran normally not shutting down like this in all of the past and it just shut down today? POOF!! Out of the blue!! Something has had a definitive change just recently IMO
I think then, your current/existing wiring as it is/was, is probably fine.
This new problem could be shutting down the motor for a few reasons here I figure,
1) Under-voltage/low supply voltage sensed at the motor, caused by
a) Low battery
b) Bad connection/s.......Check for corroded connection (as stated above) at the site of the hot spot/s, this/these spot/s are higher resistance areas and are dropping higher than normal voltage due to higher then normal resistance, V = I*R and heating up, P = I*V or otherwise put, Watts = Current x Voltage and Watts are heat.
2) Over current sensed by the motor, caused by
a) Bad bearings, rusted up locking armature, fishing line wrapped, weeds wrapped etc, etc all preventing the motor from spinning freely.
b) Shorted winding's/commutator in the armature (assumes brushed motor).
3) An in-line breaker opening, caused by
a) See 2a/2b
Since you had extra high heat/melting wires, I'd probably check 1b, if connections all look good/tight/clean, then an over/abnormal current situation is most likely concurring and then I'd move onto 2a and/or 2b.