Normally after making my shot I open the breech. Then I swab the barrel out. I then set the unloaded rifle up and will often times walk down and check the target for the hit. After taking my time, I will grab the barrel and feel how hot it is.

Depending on the outside temperatures this can take several minutes. In the summer I've been known to take three rifles out and alternate between them giving everything time to cool.

Your sense of touch would be the best judge. But about five minutes should be plenty. I'm sure Triple Se7en would have a better suggestion since he shoots an Omega and is very knowledgeable about them.