If you are running tamiya molex plug you might be getting high resistance in the leads leading to a hot battery. Brushed motors are also horribly inefficient and waste alot of power to heat especially if they are not maintained and comms kept true.
My opinion would be to get a newer car and go brushless, as they will be easier to get parts and will hold up better to brushless.
The old ultima is a great car and parts are available on ebay still but the gears are all plastic and not very stout to hold up to brushless power. If you are running a MK1 with the aluminum chassis they are also extremely vunerable to front end damage.