For those who are interested, I have found a way to work around the issue. The python-command to continue a Simulation called:
thermal_initial_global.InitializationOptions.enum.ContinueSimulation
can only take the first argument, which in my case is "heating 0". So if you now have created "heating 1" based on "heating 0", and then proceed to delete "heating 0", the only available argument is "heating 1". This will enable you to further continue your simulation. You can delete a simulation using the following command:
document.AllSimulations.Remove(thermal_sim)
given you have returned thermal_sim, of course. If you create an empty list, you can append your thermal_sim's into it and then choose which item you want to delete.
I am sure there are more elegant methods, but if you need to do this specific task, it works.