Question: We know a/c to Gullstrand's equation that the effective focal length of two lenses separated by a distance $d$ is given as $$\frac{1}{f\_{eq}}=\frac{1}{f\_1}+\frac{1}{f\_2}-\frac{d}{f\_1f\_2},$$ but the equation doesn't clarify on the position of the lens having this effective focal length, how do i calculate that?

Answer: 
It depends on where you are measuring the temperature. If your heat source heats one part of the system A, and you are measuring another part of the system B, it is indeed possible that heat continues to flow from A to B after you stop heating A - because there will be thermal gradients in the object, and diffusion of heat takes time.

So if the part of the system that is heated has thermal mass, it is indeed possible that it will continue to give off heat to another part of the system that was initially cooler. On the other hand if you were measuring the temperature of A close to the point where you applied the heat, you would find that it cools down somewhat after removing the heat, as A continues to give heat to (cooler) B.
In my own real experiment I heat a thermal mass and then observe the thermal response. What I notice is a couple of things. 1.) There is a thermal delay between the application of heat and the sensor response, this is due to thermal gradients, thermal resistance, ect. 2.) Beyond the thermal delay I notice that the temperature of the system continues to increase even though the power has been removed. I know this is true because I model the system using a first order differential response curve. My simulated model follows the empirical exactly (along with the time delay) up until the point where, theoretically the temperature should begin its exponential decline back to ambient. However, although my simulated data shows a temperature decline within the thermal delay time, immediately after the power is removed, my empirical data shows an increase in temperature long after the calculated delay time. This, in essence is a thermal equivalent of a second order response. Now, thermally speaking, this should not be possible, but as we look into thermal expansion, atomic vibrations, and other physical energy storage components, we find that in fact (and real empirical data proves this to be true) a thermal system can and does increase in temperature after the heat source has been removed. Sorry to say that Google search will unlikely be of help here because very few people are asking the question or doing the research at that level. Most will say that thermal response is simply a first order response with a delay, but mathematical simulation of closed loop proportional control will fail to match that of real world response without consideration of second order components.