Looking to cool down the transmission fluid. How effective is adding three extra quarts with an oversized pan. I do have the stock transmission cooler located in front of radiator, passenger side.
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.
Add another cooler. Water cooled stacked plate coolers/heat exchangers are awesome. Adding another cooler in line and the extra lines to and from it will add another qt or so.
There are also inline heatsink coolers that get better results than just lager pans.
Think about doing an engine coolant system- to beef it up you add bigger and better radiator, not add a 1 gallon surge tank in the system.
A larger pan does nothing to reduce temps. Adding fluid can delay the heat up by adding more fluid that has to be heated, but as stated, it also delays cooling it down as there is more fluid to cool down now. Finned and tubed pans can help as they act like an liquid to air cooler, but ones with enough added are don't really add much capacity. The factory trans cooler for the 4L80E isn't really that large. If you're after more cooling, the best solution would be a larger cooler. The B&M super coolers are very similiar to the OEM GM coolers used in the 90's, and not that hard to swap in using most existing trans lines and fittings.