No. Stainless steel is very stable and does not emit any toxic fumes when heated.
Austenitic stainless steel is annealed by heating to a temperature of about 1100 C and there are no safety measures needed regarding the emissions since there are none.
I have worked in Nuclear Fuel Complex of Department of Atomic Energy and was Manager, Quality Control of Tube Plants that included Stainless Steel Tube Plant. I am a metallurgist by qualification.