THe added pics do show that the resistor got pretty hot.
The resistor, by the way, is probably part of the DC-DC converter circuit that takes the 48V battery voltage and knocks it down to 15V to power the gating circuit for the MOSFETS, The 15V further gets knocked down to 5V with a second DC-DC converter. That powers the microcontroller and also gives you power for the sensors. I have schematics for KT controllers, and that' the only place they use a high wattage resistor, as part of the voltage converter circuitry. It means you were sucking too much power. I think most of that secondary circuitry isn't high power, but I guess that if you were spinning the motor fast/furious at top speed, that the gating circuit has to switch fast too,
Does the bike have a headlight? Did you change it out for a brighter one?
You couldn't get rich bit to give you a new controller, but you did buy one. DId it come from rich bit? How long did the second one last before it blew out? Did it run the bike for a while? What was going on when you blew it out the first time. Just sitting around and it popped, or what?