'93 mustang 5.0 starter issue

This may be an easy one for someone to answer and verify for me. I have a 5.0 with upwards of 180k miles on it and it cranks up nicely when it's sat for a while. (over night, parked at work, etc.) However once you crank it and go even as far as the nearest gas station (10 minutes for me) you had better not shut her down or the starter is real sluggish and may or may not start the engine. The battery is good, the relay is probably the last thing I replaced within a couple of years save routine maintenance parts. I suspect the starter is getting hot but I don't know what the failure mechanism is. I know it hangs just a little once you release the key from the start position but only for a split second. It's marked to get replaced but I would like to know if (for sure) and why it gets hot while cruising.