Hardenning Stainless Steels
The general rule is that the most common 300 series stainless steels are Austenitic, in that they do not repond to a heat treating or age hardenning proccess as do alloy steels, 400 series stainless steels, or precipitation hardenning stainless steels.
You can improve the properties by cold working, as in rolloing, but in general, the properties that they poccess are due to the originol alloy content.
Martensitic stainless steels, such as the 400's, respond to a regular hardenning and tempering proccess much like alloy steels.
In other words, you can take a piece of 303, 304, 316,or what ever 300 series stainless, heat it and quench it all you want, and it's properties are not going to change, other than some generized scaling, warpage or other affects of severe heating and quenching..