I've got a piece (of about 300 grams) dry-aged rib-eye in the fridge, at around 6 degrees Celsius. I want to let it "get to room temperature" (which technically is about 21 degrees Celsius for me) before I cook it up to about 55 degrees Celsius core temperature.  Is there any good rule of thumb to determine how much time I should minimally / optimally let it sit outside the fridge before slapping it into the pan? 
It is hard to tell from the picture, but this doesn't look like burned off seasoning, it is more like a burned on residue. If that's the case, you can try cleaning it some way. The problem is that physical cleaning methods probably won't be sufficient, chemical cleaning with alkali will damage the seasoning and chemical cleaning with acid, if the seasoning is compromised, can rust the pan a bit. So there is a high chance you will end up reseasoning.   If this really looks and feels like a buildup and not like exposed oxidised metal, my preference would be to soak in warm, not hot, acid. Vinegar or a citric acid solution should work well. Afterwards, try to scrub off with a stiff plastic brush.   If it doesn't go away, or the seasoning goes away too, or if this was missing seasoning from the beginning, you have to strip and reseason. We have several questions on the topic, and the Internet is also full of suggestions. I personally prefer doing it with lye (best results, strips both old seasoning and rust), owners of self-cleaning ovens like incinerating it, and there are a list of other methods to work with.  