Diode rectification on a device
If I wanted to know the voltage across the Peltier, I would measure it directly with a multimeter.

The Peltier datasheet you linked a says it's rated for a maximum current of 3 A DC.
If you push 3A DC through it, then the graph at the bottom of that one-page datasheet seems to indicate that the voltage across the Peltier should be about 0.8 V.
That's the voltage directly across the Peltier at 3 A DC no matter what other stuff you have in series with it -- diodes, resistors, inductors, whatever.

From the description, it sounds like one
Fairchild SB560 Schottky diodes b
is in-line in each of the two wires that come out of this Peltier cooler.
(I'm a little mystified what they are for, but I've already speculated on a few possibilities).

Like all diodes, it has a datasheet c.
On the first page of the datasheet, it says each SP560 has a forward voltage drop ("VF") of 0.67 V at 5 A.
But at the 3 A you're probably trying to use, the graph on page 2 of the datasheet
shows it has a forward voltage somewhat less than 0.6 V -- maybe 0.56 V?

So I expect the total voltage across the entire series chain when 3 A is going through the chain -- two diodes at 0.56 V each and a Peltier at 0.8 V -- to be roughly 1.92 V.

Honestly, that's an unusual power supply voltage.
The Peltiers I'm using this week are 12 V 5 A
(similar to d e ); and 12 VDC power is more convenient than 1.92 V or 0.8 V.