I can't see the logic in that. Usually a "bad earth" means high resistance
in an earth wire/bonding so that would mean low current and less heat. It
looks more like a short circuit from positive down to earth. I would suspect
the work done to bridge the immobiliser. Of course if you tried and tried to
start the car then that could make the terminals hot but only if they
weren't tight in the first place.

Yes you will need a multimeter but they aren't expensive. Maplin often do
digital ones for a couple of pounds. What I would do is remove the battery
if you haven't already done so and start measuring between the various
wiring points from the battery down the circuit to the starter motor. I
reckon that you will find a short somewhere. Obviously when you do find the
short you'll need to isolate that part of the circuit to find whether the
short is upstream or downstream of that point. This isn't a terribly good
description but I'm sure you get my drift.

A bad earth will mean high resistance between a part that should be earthed
and earth. You could check for this by putting a jumplead from the cylinder
block to battery negative. If the engine starts then you have a bad earth
and you'll need to find the earthing straps and take them off and clean the
connections etc.