Due to the low carbon content (<0.03 wt%), high cooling rate isn't critical. Annealing temperature range is 1850-2050 oF (1010-1121 oC), usually followed by water quenching (provided geometry doesn't cause distortion).
Biggest problem is scaling if done in air.
Scaling = Surface oxidation. Mostly from the high T anneal, but of course can be avoided by inert or protective atmosphere or vacuum.
Since Cr preferentially oxidizes, the metal immediately below the oxide is lower in Cr, so lower corrosion resistance. The oxide scale is thus removed mechanically or by pickling, plus pickling removes the Cr-depleted metal surface. Then passivate to remove surface Fe & Ni and form a more protective, purer Cr2O3 surface film.
There are TTT curves for the sensitization of stainless alloys, but since there are no phase transformations the only thing that you would worry about are secondary phases.
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Rust never sleeps
Neither should your protection
