At what speed does wind generate warming of an object due to drag, making the object warmer than the ambient temperature? At what speed does wind generate warming of an object? Say I'm outside at 0°F. How fast does the wind have to be to raise my exposed skin temperature to 40°F? Would that wind speed be so high it would strip soft tissue away leaving only a skeleton? If so, let's apply this to a thick steel pole, for example. I'm guessing there are equations dealing with air density and humidity as variables.
 A: Actually there is not an equation. This is a complex problem of fluid dynamics that includes drag and adiabatic heating from the ram effect and extremely complex friction heating and compression heating and fluid balance and convection and even conduction of heat into the core of the pole from its surface and along its axis depending upon the boundary condition. Computational fluid dynamics (CFD) would be used to model it. The “relative roughness” of the pole will matter for friction. It could be modeled if the roughness and pole material (for the material’s specific heat and coefficient of conduction) and boundary condition are all known (and of course speed and atmospheric pressure of the air). Ive done enough CFD to guess that yes itd rip you apart long before doing anything close to that level of heating. You can google the navier stokes equation to see how CFD handles the airflow problem, but then the heat balance must be added. Btw much of it would depend on how fast that rammed air could “get out of the way” and not collect and heat up much before flowing past. There will be a high-pressure, low-velocity volume there.
There are equations with empirical constants for the amount of drag, but drag is not only from friction. Even a model of a gas with zero viscosity and hence no friction generates drag, as well as heat from compression, so is much more complex than just finding the drag force times the speed of the pole (a moving pole in still air is the same as a still pole in moving air), because again zero friction doesnt mean zero drag nor heat. The gas will have rotational effects too, but some models assume irrotational. Fluid dynamics questions are usually very complex even without heating questions.
A: Maybe its best to imagine a rock falling and having its speed being damped by friction, and heating in the process.
Whenever an object has its speed being damped, its kinetic energy $K$ has to go somewhere. Some of this $K$ goes to the air, some of it heats the body. Say, for example, that half of $K$ heats the body. Then you'd have to know the body's heat capacity $C_v$ to compute its temperature change. The heat capacity tells you how much energy you need per unit volume of said object to heat it 1 temperature unit.
