Objects moving in the atmosphere gain and lose thermal energy by several mechanisms.
Firstly there is skin frictional heating, which is the conversion of kinetic energy to thermal energy due to the viscosity of the fluid. This leads mostly directly to heating of the fluid layers close to the moving body.
For high speeds, such as meteors entering the atmosphere, a more important effect is compression heating. A body moving at many times the speed of sound creates a compression shock wave which heats the air in front of it greatly due to very high and rapid compression.
Then there is thermal transfer between the moving body and the surrounding fluid, which takes place through conduction and radiation. You have a body of a certain temperature, fluid nearby that has been heated by viscosity or compression, and fluid further away that is at ambient temperature. The net energy flows between these three tell you how the temperature of the moving body changes, with, as always, heat flowing from hotter bodies to colder ones.
In some cases, one thing dominates. A meteor entering the atmosphere generates a heated region of gas that is at around 10,000K (see Why do meteors heat up when they fall through the atmosphere?) and this compressed region in contact with the meteor heats it up quite quickly.
Throwing a hot pie across the room on the other hand, is very slow moving and generates very little heating in the low viscosity atmosphere, so the dominant effect is simply the pie losing heat to its surroundings simply because it is hotter. It might cool slightly quicker than if it were stationary because a stationary pie heats up the air around and creates a temperature gradient which slows its cooling, while a thrown pie is always leaving heated gas around and moving to a region of gas at ambient temperature, so it maintains a slightly higher heat differential with its surroundings.
For a bullet, it's hard to say. If it was at ambient temperature, it would be slightly heated by moving through the atmosphere as its kinetic energy is converted in to heat (in the bullet and in the air) by drag. But the bullet is also heated by the hot gas in the gun barrel that accelerates it, so it is probably at slightly above ambient temperature when it leaves the gun barrel. But in general the calculation of just how much the surrounding atmosphere is heated (and how that hot gas is spatially distributed), and how the heat flows between the moving body and the surrounding fluid, is a complicated question that requires detailed modeling, and doesn't give nice easy answer except in very simplified cases.