At what speed does wind generate warming of an object due to friction, making the object warmer than the ambient temperature?

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. Fluid dynamics problems are very complex even without heating questions.