How do the human heat sensors work? I have been wondering about this particular issue for quite some time now. It feels like I should know this as a master's student in physics. The questions are, essentially, the following:


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*What is the physical quantity that is measured by the human skin, i.e., what is causing the sensation of hot and cold that we are feeling?


Obviously, this quantity cannot be temperature - when entering a cold bathroom in the morning, you will definitely feel a significant difference between the floor tiling and the bathroom rug, even though both should be at the same temperature. Which leads to the second question:


*Which material parameter determines whether two media that have the same temperature feel hotter / colder compared to each other?


My best shot for question 1 would be some sort of energy flux $J$, which would depend on temperature difference $\Delta T$ between skin and object and a heat capacity $c$ like
$$J \propto \Delta T\cdot c $$
so the bathroom tiling feels more extreme than the rug just because its heat capacity is higher (i.e., it loses more energy if the temperature drops). This would also explain why a regular beam of water from the sink can feel hot after a snowball fight (the dependence on $\Delta T$). Is this reasoning correct?
What is bugging me about this is that this heat sensation would not depend on the heat conductivity of either material at all. It feels though like this should play a role, but I cannot wrap my head around a way to include it.
Happy for any answer that may help.
 A: From a biochemical point of view, heat detection is achieved by proteins at the surface of nerve cells. They basically just trigger a nerve signal above a given temperature. So they DO detect temperature and not a "heat flux". It may seem surprising that nerve cells react so quickly but the increase/decrease in temperature does not need to go all through the skin. It just need to be detected at the surface of the skin and a difference of 1°C is enough to start feeling a temperature change.
Interestingly, the temperature threshold can be changed by some well-known chemicals. For example, capsaicin (from hot peppers) will lower the temperature threshold for the heat-sensitive TRPV1 protein. This is what causes the burning sensation when eating spicy food. On the opposite, menthol (from mint) tricks the TRPM8 protein (and many others) into considering the temperature is lower than it actually is, which gives this sensation of cold in the mouth.
EDIT
The initial question took as an example the feeling we all know when we enter a cold room or touching objects. This edit is meant to address that.
It is true that, after some time, all the objects in a room will have the same temperature but our skin will not, just because our body produces heat and the air surrounding us is a poor conductor. If you take a thermometer in your fist, you should read roughly 27-29°C,(1) so let's consider that it is our skin temperature, for the sake of the demonstration. Also, I will consider that everything happens while temperature is 24°C max, and 22°C in the imaginary bathroom.
We can feel a big difference if we step on the bathroom tiles compared to what we feel if we take a wooden (or plastic) object in our hand. The tiles feel cold while the wooden object feels warm. A tile is usually a decent conductor of heat, so when we step on it, it rapidly cools down our foot sole and we feel it in less than a second. By contrast, a wooden (or plastic) object is an insulator. On contact with our skin, the exchange of heat is very slow, so the temperature of our skin will not change immediately and we interpret that as being a kind of neutral or warmish feeling.
(1) Of course it depends on many factors.
