The Pentium III was the last Intel CPU where shutdown was the only possible response to overheating, when the CPU asserted THERMTRIP#. The Pentium 4 has bidirectional PROCHOT# and the Thermal Control Circuit, which divides the clock down whenever the processor is hot, and continues to run.
Only fairly recently with Turbo Boost did Intel combine both ideas. It’s actually a fairly clever optimization as single threaded workloads benefit quite a bit from the extra thermal overhead.