The ADN8831 eval board app note, AN-695, say it's designed for "medium power TECs (<4A current)".
This part controls temperature by controlling voltage on an H-Bridge. As long as we use transistors don't overheat (based on their R[DS,on] and thermal resistance), why does the ADN8831 care how much current goes through the TEC?
The part doesn't have a hard constraint on the TEC current. With the external FETs and current sense resistor properly chosen, the current can go above 4A.
ytu I'm going to try it. I'll let you know if it works and if anything smokes.
Update: It works. I only went up to 5A, but it works. I only needed to change the sense resistor and add a higher current inductor.