What common metals can be heated to approximately 250 degrees Celsius
without giving off any kind of noxious or hazardous fume or gas?  For example -
what type of metals are used in smoking pipe screens?  These clearly
would be heated beyond 250 degrees C,  yet presumably do not give off
any hazardous gases (beyond the hazards of breathing smoke to begin
with!).

My application would involve a screen/mesh of some metal material
being heated to around 200-225 degrees C. The metal must not
react, outgas or be hazardous; must remain inert at that temperature.
Heat source for my application would be secondary (i.e., not a direct
flame), and digitally controlled, so I know I won't be exceeding 250
deg C.    What types of readily-available metals are safe to consider
for such an application?

Have you considered looking at say, a frying pan?

Stainless steel, hard anodized aluminum, cast iron.  ;-)
Chugs,
Bob