Ammeter heat question

My question is would you expect them to get warm?
Roughly, 100degs?
I would expect due to resistance in the system, some heat is expected, but it surely is not enough to melt anything and would be the same even if it was left hooked up to ammeter.
No. It should not get warm.
There are only two factors in play; resistance and current.

The resistance may be higher, lower, or the same as when they were connected to the ammeter. It depends on where the resistance is. If the ring terminals are oxidized., if the wire and crimp to the terminals has been damaged, these will cause the same resistance regardless of whether they are attached together or bolted to the ammeter studs.

The current moving through the circuit is the same whether the two wires are connected together or connected to the ammeter.
The only current that should be going through that circuit is when power is needed to start the car, and when the battery is getting recharged.*

Starting will draw no more than 5 or 6 amps though the circuit.
Recharging will draw anywhere from 10 to 20 amps very briefly and then quickly go down to roughly 5 amps, and then eventually zero.
If you see more than this on the ammeter, then the problem is not the circuit, but a high load problem.
With the ammeter disconnected, you can put a clamp type ammeter on the line. (Do not support the meter clamp with the circuit wire!)

On the other hand, if the ammeter is indicating normal operation, and the connectors are getting warm, then there is excessively high resistance.

*There are a couple of exceptions; clock circuit and convertible top were sometimes tied in at the ammeter.