My new apartment has an older gas stove--I'm guessing its from the 70s? All the markings are gone. Anyway, on the stove top there are two hot spots where the pilot lights are underneath. It's hot to the point where you cant hold your hand there for more than a second or so. The pilot lights are not huge, I'm estimating a half inch tall, but there is zero insulation. There is just a thin metal piece in between the stove top and the pilot. I'm assuming standards were a little more lax 50 or so years ago. It seems like a fire hazard to me. What do you guys think?
This is not an improper fire hazard. In operation the stove top near a burner will get a lot hotter than that.
You are not supposed to lay flammable materials on top of the stove, but I doubt it would start a piece of paper on fire. You could place a 1 inch square of paper towel over the hot spot and see if it would ignite.
AFIK modern gas stoves have electronic spark igniters (they do not have standing pilot lights) so one cannot compare modern stoves to old ones which do have a standing pilot light. I don't think a hot spot over a standing pilot light is an out of specification condition.
It is not a hazard, the complete top of the range is considered a cooking surface and that would be totally normal if the length of the standing pilot flame is as you posted and the actual cap is intact on the burner assy. UL is who determines what acceptable temp ranges are for products. From what you described, that is the standard for the front and rear burner assy with a standing pilot.