250F for the oil is perfectly fine. (And I'm not sure what the car being N/A or turbo has to do with the temperature being too high or not.
) I've seen as high as 270F or so. Adding an oil cooler wouldn't be a bad idea, but it certainly isn't necessary. Adding the OEM oil-to-water cooler on my car dropped my peak oil temps from ~270F down to ~250F.
As for the coolant, on most overflow bottles (not sure about your year/model) there are 2 FULL lines - one for COLD and one for HOT. If the car is cold and the coolant in the overflow is already at the FULL-HOT line, then it's not surprising that it would end up a few inches above that when you come off track.
Pat Olsen