Can't imagine heat changing the properties of your stainless, I worked in an abbatoir for a while as a fitter/welder. everything was made from food grade stainless, the heat from welding never changed it at all.
if it was me, I would go with the drop saw. just let the weight of the saw do the work dont try to force it through. then clean off the burrs with a file
you never stop learning, till the day they shovel dirt on your face