For the source text click/tap here: Chullin 111
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After discussion about the matter the Gemara cites Chizkiyah in the name of Abaye who rules that one may eat fish with dairy even after the fish had been placed on a meat plate while yet hot.
This is called “nosen ta’am bar nosen ta’am” or “nat bar nat” and refers to a circumstance in which a taste has been transferred twice. In the Gemara’s case it refers to the meat taste that was transferred to the plate and then from the plate to the fish.
Tosafos (1) relates that Rivan explained in the name of Rashi that if the fish was cooked in a pot that had been used for meat one may not eat the fish with dairy.
The reason to distinguish between fish placed hot on a meat plate and fish cooked in a meat pot assumes that cooking transfers more taste than contact between a hot food and a cold pot.