Voltage Regulator Malfunction???

So I was being proactive and while the 318 in my 68 Barracuda was warming up, I stuck a voltmeter on the battery terminals. I was showing 15.06 - 15.13 volts. Pretty sure that’s too high. Shouldn’t it be more like 14.2 volts? I don’t want to cook a battery - they’re getting pretty spendy nowadays.

Located my voltage regulator but it doesn’t look like what I was expecting. Is this some sort of solid state replacement for the big brick I was expecting? What should I be looking for as a replacement? This thing only has the two wires going to it.
Appreciate any advice! Thanks.
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That's pretty typical cold at start up.

The regulator on the car is a solid state replacement. While it looks like the MP P part painted black, the numbers on the top indicate its probably made by or for Standard Motor Parts or such.

You can do the test suggested above to determine if there is resistance in the run circuit. However with that regulator you will have to back probe the connector with red wire. Note the ammeter position when you do the voltage drop test. It should be slight discharge, but people sometimes tap into that circuit for additional stuff (such as electronic ignition, electric choke, stereo, electric fan). Those will increase the current a little or a lot.

Some other test you can do are:
a. Measure the voltage at the battery once the battery is charged. You'll know its recharged by looking at the ammeter.

b. Measure the output voltage of the alternator. If its the same as the battery during charging, then suspect a drop in the run circuit. If its higher than the battery during charging, then suspect the alternator output and battery charge lines. A variation on this test is to get the battery charged, and then add accessory loads such as the headlights and heater fan. Without a relay harness, lights will add a load of 12 to 15 amps to the output circuit.

Back probe into the input connector on a SMP VR-128

Another issue that comes up is with replacement alternators. Replacements, especially the revised squareback, have a higher field current draw than the originals. I wrote to SMP to ask for the specs on the VR-128, and they only had the dimensions. :( It would not be surprising that the electronics can handle 3 to 4 amps fine, but not 7 amps or more.