Mix the polenta with the cold or room temperature milk using a whisk. Turn on the heat to medium and whisk constantly as polenta can stick to the bottom of the pan and burn; specially once it has started to boil.
Once it has thickened enough, try it. If it still has solid grains left, add a bit more milk and keep cooking. Otherwise, add the parmesan cheese and whisk until melted
Taste it and adjust the level of salt (the parmesan has salt, so that's why we wait until after adding it to add more). Finish with the butter and serve hot.
If you're going to reheat the polenta afterwards, make sure to put cling film on top touching the surface of the polenta so it doesn't form a crust. You'll definitely need more milk to thin it down while reheating.