The smaller no. means bigger cable, e.g. 12AWG is bigger than 14AWG, also the bigger cable allows higher current passing thru at the same time, thus less heat!!
oh in this case, I think your ESC is 12AWG and your battery is 14AWG, it is not easy to change the cable on the battery, do you have a battery with bigger cable?? BTW, what A no. is your ESC e.g. 60A or 120A??
wo 120A and 4T, you must be using around 50C - 60C batteries right??
I thank the cable on your ESC should be ok, if the battery cable is the plug type, you can just buy 12AWG cable with plugs, if not you may need to buy a new battery!
Also make sure the fan of ESC is working ok, the car stop may be due to over heat, plus it is Summer in HK, so you may need a bigger fan too!!