Starter motor running slow

Earth lead has a poor connection from the battery to the starter. high resistance
thats why it is getting hot. check all connections and joints for volt drop on earth lead.

Gary

the crimps on the ends of the cable would have got very hot as well, you will probably need to replace the whole earth cable and clean the surface face on the body where the cable connects.
regards

As said bad connections on either the negative or positive cables, starter solenoid switch contacts, starter brushes or glory help us all, the engine is starting to seize.

Hope you can find the problem.

Andy, it's highly likely the bronze bearings on the ends of the armature are worn, allowing the armature to drop and contact the field coil magnets ("pole shoe" in Delco-Remy terminology), making the starter "pole out", or short out.
The clearances between the armature and the electromagnets screwed to the housing are small, even when new - and any wear in the bronze bearings will reduce the required clearance to virtually nothing, making for a short-circuit condition.
The simple cure is new bronze bearings both ends.

A good starter motor repair shop in the old days, would always keep these bronze bearings on hand.
However, it's hard to find anyone who will even repair starters today - let alone keep the bronze bearings in stock.
I have a drawer full of them, I bought most off eBay when people were selling deceased estate stuff from old electricians that had passed on.
You don't use them very often, but they are manna from heaven when you have a wonky starter like yours.

If you take your starter into a dealer or electrical repair shop, they will just tell you it's stuffed and want to sell you a brand new one.
And the reason they do that is because they can no longer repair starter motors at a price below what new ones sell at.

Cheers, Ron.

Andy, there are two clues in your expression..... 1) "the starter is hot but not extreme" and 2) the earth lead has "melted from the connection at the battery".
If the starter is not extremely hot suggests that there was not an excessive current flow through the starter and accordingly, not an excessive current flow through the earth lead. Therefore the heat was generated not by excessive current but by excessive volt-drop in the earth lead, almost certainly by a poor connection at the battery which would account for it "melting".
Either remake the earth lead connection properly or replace the earth lead with a new one.