If firing a gun in outer space was a regular occurance I think somebody would of thought up something in ceramics by now.
Of course until that happens we can always rig up something like the water jackets on the old Brownings.
I would imagine the gun would heat no quicker in space than on earth. I saw a thing recently on TV where a guy set a record for fastest firing of a pistol (revolver). It was a special Smith & Wesson competition pistol with eight rounds. The guy fired all eight rounds in something like 1.1 seconds (IIRC). I doubt that the earth’s atmosphere had much chance to cool the pistol in that time and the pistol had no problems handling that rate of fire. You should be able to do the same in space without a problem.
Your problem occurs if the person wants to continue rapid fire, reload, rapid fire, etc. Again I would wager you could get nearly as many shots off in space as on earth since the cooling by the atmosphere won’t be that great before all that firing heats the barrel too much. In the end you might get a few more rounds off on earth but I doubt too many. Where you win out on earth is how long you have to wait before being able to fire the weapon again (much shorter on earth).
As to recoil it may be an acceleration ‘backwards’ of only 1/650 the rate of gravity but if you are firing a machine gun each round adds to your acceleration. A pistol with 6-12 shots may not net you too much acceleration but a machine gun with enough ammo could act like a small rocket pushing you backwards. Imagine firing a minigun in space. At 4,000 (or thereabout) shots per minute you’d reach an acceleration equivalent to gravity on earth in about ten seconds of firing (assuming the recoil figures given above although they are undoubtedly different for this type of gun). Of course a mingun is a bit much to handle for one person unless it is mounted but in zero gravity it could probably be done.
Here’s a link that shows what a muzzle brake looks like.
http://www.berishguns.com/custom_muzzle_brakes.htm
Actually net heat loss by radiation in ordinary circumstances is almost negligible. You are usually surrounded by objects that are only a few degrees cooler that are radiating back at you. An exception might be in the middle of a field during a cloudless night. There you’ll be close to 50% of the way to what you might experience in the way of radiation loss (upward), sans vacuum, that you would feel in space.