I have now implemented a UDF for the effective heat capacity which just computes a derivative of the specific enthalpy and multiplies that one by density. It seems that indeed this was the route to success - my simulation runs now, I will see what result I get.
@NJank: My conclusions are the same as yours. I also did introduce some debug print statements in HeatSolve.
Normally you should not need a full Fortan development environment to compile ElmerSolver, but as stated in the other thread mentioned above the available compilation instructions didn't work for me. I still hope that sometime soon, the Elmer Windows compilation guru takes the effort to update the compilation instructions. I will be happy to serve as test person...
BTW, I use a UDF calling another one for the heat capacity. In case someone wants to know how to do that, I will update this thread http://www.elmerfem.org/forum/viewtopic.php?f=7&t=2288 in a minute.
Thank you again Peter and NJank for your assistance!