The cooling system itself is sufficient for that particular model and moves some decent air across the heatsink. It should not have been able to heat up to that point even if the fan is seized on that particular model it usually won’t hit the thermal shutdown point unless something is preventing proper transfer of heat.
This could be caused by dust caked on the heatsink. Or poor quality thermal paste (Or tape as it’s a dell) between the heatsink/cpu which has a tendacy to breakup over time from the factory.
If it’s clean and does it again, remove the heatsink. Apply some good quality thermal paste. Put the heatsink/shroud back in. And you should be in business.