#Python, 78 72 66 bytes
Python, 78 72 66 bytes
Pretty much a direct implementation of the algorithm provided in the challenge description.
lambda T,r,w:T+.0201465*r*2.7182818284**(17.27*T/(237.7+T))-.7*w-4
This was specifically tested with the maximum value of T
to find how many digits of Euler's constant were required for the error to be within the allowed amount.