Welcome to TechIMO!
Thermal protection is not a failsafe, and I am honestly surprised your P3 chip is even stable at such high thermal loads. They are well built processors, but you are pushing the limits.
By standard cooler I will assume you mean an Intel retail heatsink. The stock Intel P3 cooler is usually a decent heatsink, even for moderate overclocking. Are you using thermal paste, or the thermal interface pad supplied with the heatsink cooler? If you are using the pad, then remove, then apply quality thermal paste (Artic Silver or Ceramic recommended) for improved thermal transfer.
Honestly, it seems like you have a decent overclocking chip, you just need better cooling. Quality heatsink coolers for overclocking the P3 can be found for under $20 these days.