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There is an informative paper available on the Micrometals Inc. website titled “Iron Powder Core Selection For RF Power Applications”. It says the following: “It is important to limit the operating temperature of inductors and transformers using iron powder cores. Long term operation of iron powder cores above 80 °C can cause a permanent reduction in both Q and inductance”. That’s 176 degrees F.
Note that it says “long term”. Short term temperature can go higher without causing damage, but there is no data on what the temperature limit is for a short term. The document does say that intermittent temperature peaks can be averaged over time and the average shouldn’t exceed 80 degrees C.