My routine is to fire no more than 15 rounds through any rifle without cleaning. Many DCM matches don't allow for any cleaning. DCM competitors regularly fire up to 70 or 80 rounds between cleanings. Such rifles, though, generally sport barrels of larger diameter allowing for better heat dissipation. Fired rapidly enough, any centerfire rifle barrel will become hot to the touch.
Heat is generated in direct proportion to the quantity of propellant burned.
Smaller diameter bores, even magnum .30 caliber chamberings, will become hot to the touch from a string of rapidly fired rounds as few as a magazine full. Here, I refer to sporter hunting rifles holding no more than five rounds. It's quite normal. If the original sights cannot be adjusted to allow the rifle to shoot to the point of aim, consider the installation of a receiver sight from Williams or Lyman. A gunsmith will need to drill and tap the receiver for such a sight, for a nominal charge.