It does appear that the simplified model is only relevant for the simulations. To quote Heinert: "An efficient computation is only possible for the simple model, as the advanced model would require an element of size more than 106 ." I have run Koji's code that replicates Heinert's figure 3. I have attached the resulting temperature distribution and noise amplitude curve. In the noise amplitude curve, the red line is the analytical result, while the dots are from COMSOL.
The next step is to convert this code to an efficient complex time-independent solution. As stated before, my main concern here is whether COMSOL actually solves the right equation in the stationary case.