Please excuse the title of the question, there is physics involved here, but I can't think of a way of writing the title without it being more to the point of the question.
A cowboy film is pure drama, and I don't normally expect any correct physics to come from Hollywood. My question is based on watching old "Gunsmoke" episodes during which, each time an actor is shot, even if he is hit in the body far away from a vital organ, the movie doctor says words to the effect "That bullet has got to be removed now".
Far more important though, is that this may also be the case today, I just don't know.
My question is: if the bullet is powered by a very hot stream of gas to fire it, after which it travels through the air at an average speed of 1,700 mph (2,740 kph), where friction from the air slows it down, (but may also heat it up), then the bullet may be essentially sterile in the short time it takes to hit the "cowboy", and unless it's lodged near the heart say, I wonder am I correct in assuming there is no rush to remove it?
In fact, the bullet may be so hot, it may cauterize the affected area.
Over longer distances, say from a rifle shot, this may not occcur and the bullet may well be air cooled enough be a source of infection. This is simply a guess on my part though.