Older gas stove is hot to the touch
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.

EDIT

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.