Is is safe to assume you are touching the socket while the light is off?
It depends on what the source of the heat is. Many lamp sockets, especially ceramic ones, can work in searing heat created by large incandescent bulbs. So, if the heat is from the bulb and the bulb is not larger than the lighting fixture's rated power, then there is nothing to worry about.
But If the bulb is not terribly hot itself and/or flickering or is dimmer than its power rating would suggest, then there may be a problem with connection inside the socket which may have increased resistance and therefore created heat <strong>inside</strong> the socket. That would definitely be an issue. If that's the case, I would start by simply unscrewing the bulb and screwing it back on to see if there's any removable debris in the socket, and if that does not help, the socket will have to be taken off and looked at or simply replaced - they are usually not a high value replacement part by themselves. <strong>Any actual work on the socket has to be done with the circuit shut off at the breaker panel.</strong>