Heat makes electric motors less efficient. The ideas posted above are good ones.
It is expected that it won't work quite as well hot. Almost any deficiency in the starter or cables will show up worse when it is hot.
The solenoid can run out of copper on its switch contacts. Most often the symptom is just "click click" rather than running slow, but I have seen slow running also. Heat makes it worse because the metal bracket expands inside the solenoid and pulls them ever so slightly further away. These contacts should be inspected anytime there is starter trouble.
A starter with bad bushings may drag worse when hot (the armature is a tiny bit bigger due to heat expansion, and might start dragging on the pole pieces). The bushings should be inspected. Also the brushes. They could be wore out.
Heavy battery cables (as originally equipped) are necessary for best starting. In fact, too small cable is the most common problem on 6 volt starters.
