Shockwaves cause a temperature increase
Another thing to note is that the air crossing the shockwave created slightly ahead of a supersonic body is heated significantly. Air crossing a Mach 3 shockwave (roughly 3300 fps) jumps up by a factor of about 2.68, in Kelvin. So 85 deg F air going into the shock comes out at 1,002 deg F. Pretty damn hot. Now this assumes a normal shock, ie. that the shockwave is flat and perpendicular to the bullet path, which it isn't. Bullets create an oblique shock, which is has a smaller effect on the temperature, but it's still significant. For a bullet with a 40 deg angle on the nose the temp increase is still 2.00, so 85 deg air becomes 631 deg.
(For non-engineers; how 85 times 2.68 equals 998.3)
85 def F = (303 deg Kelvin)*2.68 = 812 deg Kelvin = 1,002 deg F