Great clue; kudus to you for noticing this.
Check your mechanical advance springs.
If the ignition timing fails to advance, two or three things will happen;
1) engine will lose power, and
2) water temp will go up. This is for two reasons;
a) because with the loss of power, you now have to press the gas-pedal harder, to achieve the same work, and
b) because the heat of combustion is carried lower in the cylinder, transferring heat to the water longer and also firing it into the exhaust manifolds, meaning it has to go thru the exhaust ports which have very-close proximity.
BUT
if the flyweights freeze in the full advanced position then you have different problems, namely;
1) a higher than normal idle-speed
2) difficult hot cranking
3) probably mid-rpm detonation
4) possibly a touchy gas pedal
5) runs just fine at WOT after ~3600rpm.
6) but probably NOT extra heating.
But broken advance springs, or frozen timing are not the ONLY things that can cause a sudden power loss together with an abnormal heat signature...... How's your transmission behaving? lol.
BTW
the last Line-Loc I bought was about $50............... but to be fair, that was 1971, lol.