I just got done towing a 5000lb TT (23') about 400 miles from CA to AZ, after running 55 on the freeway for quite a distance, a lot of uphill, and then stopping for gas, the diff cover was only warm to the touch and the diff housing was hotter but not "hot." I could keep my hand/fingers on it for multiple seconds before it felt "uncomfortable."
As for OK temps, 200-290F I would consider to be OK and normal, with the higher end being under heavy load. In order to be API certified for their specific rating, such as GL-5, lubes and differentials are tested at different loads and speeds with temps ranging up to 295F. If there is any damage to the gears or bearings, the lube fails certification.