RC Battery connectors can get very hot and can even melt when too much current is flowing through them.
This often happens if you are using a powerful Motor/ESC system that draws a high current with connectors that are designed for stock motors and lower currents, such as Tamiya style connectors (pictured below).
Tamiya Style Connectors (Low current battery connector)
Tamiya battery connectors often come fitted to Ni-Cad and Ni-Mh battery packs – especially in ready to run RC packages.
Upgrade to high current battery connectors
The best thing you can do is upgrade to high current battery connectors. A few examples of high current connectors are shown below: Deans (popular for rc cars), EC3, XT60 (both popular with rc planes) and Bullet / Banana type gold plated which are great for cars and easy to solder on.
Once you have fitted your new connectors, not only will it solve the problem of battery connector meltdown, but you should also notice an improvement in performance, because the lower resistance of the high current connectors means less power wasted as heat.
Note: Always try to buy genuine connectors and not copies. Cheap Chinese copies of XT60 and Deans connectors can melt when you are soldering the wires on, and the plastic can be brittle or weak.
Also see related guide RC motor wires getting hot or melting.