Adiabatic temperature change vs Kinetic Heating
First.
At stagnation point, the flow is at zero speed relative to the body for a very small layer of molecules at the surface of, f.ex., the leading edge. This means that this amount of still, warmer air is too small and will not affect the main airflow.
Now about stagnation temperature.
The air is a compressible mix of gases which changes characteristics as speed is increased. At subsonic speeds the air is thought to be isentropic and therefore the first law of thermodynamics can be applyed. That is that as the dynamic pressure decreases (velocity/IAS) the static pressure and temperature of air is increased and vice versa. All this happens adiabatically, meaning without any energy loss (heat) from the system. Because of all this, the stagnation temperature will be equall to Total Air Temperature.
TAT=SAT+Ram Rise
So Ram Rise is what we measure with the rule of thumb mentioned above..
(The exact formula is RR=TAS^2/2Cp , TAS in kt, and Cp is the specific heat for constant pressure, so a more exact rule of thumb would be
RR=[TAS/87]^2 ) These equations do NOT take account for Kinetic heating
Ofcourse there is always some friction from the air and this is what is called Kinetic Heating/Aerodynamic Heating but for subsonic speeds this is almost negligible. The modern TAT measuring probes have a recovery factor q=0.98, so the ADC of the aircraft multiplyes the above equation with q to get the correct TAT.
At supersonic and hypersonic speeds the equations used for measuring TAT are different as the air starts behaving as a non isentropic fluid.. Meaning that the Stagnation temperature will not be equal to TAT..
Jetpipe.