A thermally conductive gap filler does not conduct the heat as expected. Where does the heat go? I have a mug warmer, which is a hot plate that I've measured heats up to 56C.
It came with a mug with a flat bottom, which gets its contents warmed up to about 53C after some minutes.
My understanding of the sytem is that the 56C of the hot plate is a boundary condition that would force the mug to eventually reach that same temperature if there was no heat lost to the environment. But of course there is some heat loss, which is why the mug stabilizes at about 53C.
Now, I have added to the hot plate a 5mm layer of a compressible thermally conductive gap filler, which is normally used to fill the gap between a heat-generating electronic component and a heatsink; my goal being to be able to use mugs with a non-flat bottom, like any off-the-shelf ceramic mug, while still having good thermal contact.
The problem is, I found that somehow the gap filler is not transferring the heat as much as I expected even when there is full contact, and I don't understand why.
The surface of the gap filler gets as hot as the hot plate: 56C.
However, even the flat-bottomed mug on top of that flat gap filler gets only to 41C, no matter how long I wait.
As far as I can tell, every surface here is flat and having good contact.
So, how to explain the fact that just introducing the gap filler lowers (so much!) the maximum temperature reached by the same mug? It's as if the filler is sinking part of the heat, which makes no sense - right? So, where does the heat "go"? What am I missing?
Adding some detail:
The mug is about 10 cm high and 8 cm in diameter, so its side surface is about 251 $cm^2$. It is not double-walled, so it gets hot in every case.
The gap filler is a circle, 5 mm high and 5.2 cm in diameter covering the hot plate, so its side surface is about 8 $cm^2$.

 A: 
So, where does the heat "go"?

Into the surrounding environment of course!
Sounds like your hot-plate is temperature controlled. (I.e., it's surface temp will never exceed 56C.) If that's the case, then you should expect that the the temperature of the mug to be less if you put any kind of insulating material between the mug and the hot plate: Slowing the heat flow will not increase the temperature of the hot plate, but instead will slow the rate at which the temperature control allows heat in to the hot plate and eventually, to the mug.
My guess is that your "gap filler" is a better conductor than the air that it displaces, but it doesn't conduct heat as well as direct, surface-to-surface contact when you use that one special mug.
A: Heat may be lost in any number of places other than directly to the contents in the mug.

*

*To the air surrounding the sidewalls of the gap-filler. Your experiment with the original flat-bottomed mug does not include this loss. To minimize (remove) this part, you should also insulate around the edges of the gap filler. Given the thickness of the filler pad, this is likely the greatest loss.


*To the side walls of the mug itself, whereby it then goes to the air surrounding the mug. This loss will be evident when you change to different mugs.
In your system, the heater likely has a limit to supply a fixed power (to avoid blowing up). This is a limit to the heat flow (current flow) for the case without and with the filler.
The two pictures are below, with $h$ as heater (fixed source), $f$ as conduction through the filler, $l$ as loss from the sidewalls, $m$ as conduction into the mug, and $c$ as conduction/convection into the contents.

A: Gap fillers for use in semiconductor-heatsink junctions are typically filling gaps that are of order 0.5mm or less in thickness. At 8mm, that gap filler layer is far, far too thick. As such it is interfering with heat transfer, not enhancing it, by leaking heat out through its thick side wall. The surface area of the leak path is, as you say, about 8cm^2. Compared to the surface area of the top surface of the gap filler slab- 21cm^2- it is significant!
