Temperature dependent Heat Source (Integral equations)

Hi guys,

The topic seems to not make sense at first but hopefully the following will give some enlightment.

I am trying to predict a capacitor's end of life and in doing so, I need to create an equation for the heat source with various parameters. One parameter in particular (which is the Equivalent Series Resistance) depends on the temperature of the core (for simplicity, the solid surface temperature). Now the equation I have is an integral which depends on a specified temperature goal.

Is it possible to include an Integral equation in a function heat source. And if not, are there any alternate methods?

Thanks.