General commentary is that there are pro's and cons.
More fluid is generally a good thing. Better thing to focus on is a healthy tranny as more fluid will not help a failing system. Without knowing the scenario that is getting your tranny hot (ex: just highway cruising or pulling hard) it is possible that a larger pan will not help and only mask the issue.
When towing, having more fluid is more mass to extend the time that it takes to get hot, and at the same times extends the time to cool-off after cresting the peak.
And unless I am missing something, just adding 3 quarts will not help the tranny run cooler as temperatures will still fluctuate at it's normal operating range (based on load).
Toward experience with a larger pan, I have one (IIRC Mag Hytec (bought it a few years ago)) that was installed when I got a new tranny (actually, re-man but only re-used the case and pump); also, I re-used the OE aux cooler. Since the new tranny, have pulled my 6,500# RV up long 5 - 6% grades during the Summer with A/C 'On' and the TFT did not go much over 220 even though the TCC was unlocked and speeds got as low as 20 mph in 1'st gear.