If you worry, can wrap the gas hose with the insulator, like the type use on a/c, forgot the name. Check the heat ratting.

Some place sell heat insulator for hose too.

I think the build in over heat dissipation are on the front. If you don't use the over for long hours will be ok.

SS pipe also conductive, and also heat conductor, SS because of its price. Bending will have problem for SS if not done correctly. For non expose area copper were used, even on gas burner internal. Expose area many uses GI Piping for its strength and price.

AC Pipe also use copper, open up rinnai or any gas water heater, internal also copper. Even Instant water heater internal is also copper.