What exactly are you referring to when you state "Imax"?

OK. For some reason I thought you were talking about Imax theaters.

The letter I generally refers to the current, with designating the maximum current that can safely pass through a device. Your reference to Ohm's Law also suggests that you are talking about the current and not the power. They are two different concepts.

Specifically for a Peltier device, on a spec sheet would refer to the maximum current that can pass through the p-n junction without burning out the device. However, the amount of heat (difference in temp. between the "hot" and "cold" sides) is roughly proportional to the current, so the larger is, the greater difference in temperature one can achieve.

You are continuing to confuse the concepts of power and current. These are two very different concepts.

For a given p-n junction, the heat transfer is proportional to the current through the junction. That is the mechanism by which the Peltier Effect works. However, most Peltier devices are made up of several junctions. Also, different Peltier devices may be made from different materials, so you cannot compare one to the other in the manner you suggest. If you measure the applied current vs. the change in temperature for the same device, then the relationship will be linear (or at least close).

When you look at the spec sheet for your device, does it say the following:

= 38 W

I would be very surprised if it did.