Maybe strip back more of the insulation from both wires you're soldering so you have a larger contact patch between the two ends when you re-solder it.
Resistance causes heat. You will need to find a way to remake that wire connection that has a good enough connection where it won't build up heat. Yeah, you could "take it easy" on the throttle, but where's the fun in that? Looks like that connection is soldered, but probably needs a better soldering job. It might actually be cheaper to take the rig into whatever local hobby shop you have near you and pay them to solder the connection, than to buy a new ESC. I've had work done at Ray and Robin's Hobby Shop in Falmouth and they are extremely reasonable there.
