Hello: An acquaintance has a pond with many bluegill (I do not know which variety). He feeds them and all the other pond fish on pellets purchased for that purpose from a local feed store. The bags are around 50 pounds. My guess is that you can feed them like a large cichlid.
Years ago I saw a bluegill tank in a biology lab. The key item was that it was refrigerated to keep the water cool. That was one reason I never kept this native type as I did not want to invest in a cooling unit.
I know from my topwater flyfishing that the smaller ones can tolerate warmer surface water in the summer at least for a while. It is more common to catch larger individuals in the spring and fall in the shallows. I think the smaller ones may stay in the shallow warm water to avoid being eaten. There is less dissolved oxygen in the warm water and the bigger fish tend to be found deeper as the summer progresses. You may consider collecting your fish from a warm water pond as they might be more acclimated to warm temps.
You also may want to check with the local wildlife authorities about collecting a native species. When I did a field study in the 70's, I had to get a permit to collect fish from some local creeks.
One other thought. If you keep these fish and some day decide to get rid of them, it may be best to put them back in the same place they were collected from. While bluegills are so wide spread that it is unlikely to cause problems wherever you let them go, it may be possible. Released oscars have established breeding populations in Florida waters.