Like Turbo pointed to, a bad connection acts like what we could call a dropping resistor. All the voltage and amperage would be seen across it, producing that effect.
If you put a volt meter on the battery post and at various positions as far back on the bare copper of the cable as you can, you shouldn't get any voltage. If you get battery voltage the cable needs cleaning.
An example of the same would be, a test light connected between the positive post and ground. If you put a meter across the bulb, you'd read battery voltage.
Yet another example was a house outlet in a place I was renting. There was nothing on the outlet, but it was so hot you could not put your hand on it. After scratching my head a bit, it dawned on me outlets were daisy-chained, so an outlet down the line and with something on it, in my situation, an alarm clock, drew a little current, so completed a circuit. That was enough to cause a bad connection (aluminum wiring) to get hot.
I cleaned the connection up (in the house situation, that meant copper pigtails with deox goop between outlet and aluminum wire, and the problem was gone.
IF the problem was the main cable to the starter, and if the connection was bad, it should get hot really quick.
If not starting [and pulling a lot of amps through it], the wire should not get hot, because there is no complete circuit between hot and ground.
All that aside, the first place I'd suspect being a bad connection would be the hottest part of the cable, which you indicated was at the battery. That seems reasonable, since that's the most common place for corrosion, just as with all the green crap most of us see on battery terminals.
Of course, it wouldn't be a bad idea to check the other end too, WHILE you have the connection at the battery open.