A turbo can run very hot indeed so that doesn't surprise me. Most modern turbo charged cars run the oil through the turbo for a few minutes even after turning the engine off for this very reason.

Is it normal for a turbo to get hot?

Totally normal for the turbo to get steaming hot after any amount of driving at temperature. In fact, it's pretty normal for the engine bay to be very hot in general. Increasing the amount of power while decreasing displacement causes the heat density to increase, exacerbating the issue.

Do turbo cars heat up faster?

Senior Member. In practice, under normal commute conditions, turbo vs NA will have little difference on HVAC performance.