No, CPU's don't have that problem these days. In the worst case scenario which is running the CPU without a cooler on it, the system will shut down if the absolute limit is reached. For current gen Ryzens the thermal trip limit is 115C.
Ryzens will run as fast as possible (within set power, temp, and current limits) up to 90C (95 for 5600X), which scares people who don't understand that this is by design. If cooling is not sufficient, the CPU will clock and volt down to keep temps from exceeding that limit.