[Baz]

OK let's see if this helps.

From what you wrote - there are 2 cables coming from the transformer. A cable is two wires molded into a single cable.

One cable works - the other doesn't.

These were to feed two light fixtures.

You know what? If your light fixtures are LEDs - you probably only need one of the cables.

Disconnect both cables at the transformer. Attach a light you know works at the cable end you said doesn't get hot. Then attach each cable - one at a time - until you see the light come on. Then go ahead and just use that cable and leave the other one unattached - and abandoned.

You should be able (like I said) to run both your light fixtures off the one good cable.