Is there any restriction on using Equivalent Thermal Circuits? As you know, we can use thermal resistance to facilitate the solution of many problems concerning heat transfer.
https://en.wikipedia.org/wiki/Thermal_resistance
http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node118.html
But is there any condition that should be met before we can use this concept? 
 A: Such tools are approximations, and as such they always have regions where they work well and regions where they do not work well.  Equivalent Thermal Circuits work well enough that we use them a lot.  They work because the underlying equations for the transfer of thermal energy and electrical energy are similar enough.
However, that doesn't mean that the circuit you need to solve is simple.  If you are dealing with transients or heat transfer between two continuously changing heat gradients (like in a heat exchanger), the circuit can become complicated enough that you don't necessarily want to solve it in that form.
The heat exchanger points to one major limitation of using circuits like this: moving material.  In electronic circuits, the batteries and capacitors and resistors tend to stay fixed in place.  In a thermal circuit where there is fluid flow, the simple circuit model breaks down.  In electrical circuits, that starts calling for active circuits which are messy, and you eventually reach a point where it just isn't worth going for the electrical metaphor.
