Which one really determines how people feel. Heat or temperature?
Regarding the last part "Do we feel heat or the temp?" - this is more physiological then chemical, but I want to share this anyway.

We feel heat flux, i.e. how fast heat is removed or supplied to our skin. Since heat flux can be both advection in the surrounding medium (e.g. air) or conduction in the skin it depends on the situation which is dominant.

In general you can write this as 
$$ Q=k A \Delta T$$
where $Q$ is the heat flux, $k$ is some transfer coefficient, $A$ is the exchange area and $\Delta T$ is the temperature difference. The value of $k$ depends on the mechanism of transfer e.g. for advection it scales with $\rho C_p v$ i.e. it depends on the heat capacity and flow velocity of the surrounding medium.

The consequence of feeling heat flux is that we can only feel temperature differences not absolute temperature and that advection gives rise to a phenomenon called 'wind chill' that causes us to feel colder when there is more wind, because the higher wind velocity increases the heat transfer coefficient.