Yes it is possible to multiply two analog signals using operational amplifiers.
The circuit includes
I/P-1----> Log Amplifier 1-----> | Adder |-----> Antilog Amp.-----> O/P
I/p-2----->Log Amplifier 2-----> |______|
The output is multiplication of two analog I/P's.
You can find log amp., adder, antilog amp. in any op-amp text book.
But doing all this stuff just for cooling is useless. Its better to change the position og reglator IC and mount it on appropriate heatsink.