circuit determining consumed energy

Hallo all,

I have a Wheatstone bridge, which is biased under a constant voltage. 
One resistor on the bridge is a heater made from tungsten. The 
resistance of the heater varies with the environmental temperature. When 
the heater is cooled, the current through it will increase, i.e. the 
extra energy is consumed during the cooling. I'm seeking for a circuit 
which can be adopted to measure the consumed energy of this resistor. It 
would be thankful, if you could give me any tips on it.

Thanks in advance,