TBH, I don't see why it would be a problem.
The OP has said that the actual trap he's going to put him in is bigger than the bowl itself. Plus, he's getting a heater and filtration. All in all it sounds like a big improvement on the bowl to me. The betta might actually enjoy his holiday in the big tank!
I myself have just been temporarily housing my betta in my community in a breeding trap while I used his 5 gallon to treat a sick fish. I had the option of a clear plastic box or a net, and went with the box, figuring if he needed his vision cut out more I'd use the net. At first he seemed fascinated by the existence of all these other fish! He usually lives alone. Of course all the other fish were interested in him at first too, and came up to look at him the first day or so. Then some flaring ensued, especially at the pearl gouramis (long fins kinda = other bettas). But now everyone is over each other and aside from the occasional flare (which he did by himself before anyway) all is peaceful. He's even blown a few nests while he's been in there. But as soon as I finish cleaning his old tank (the other fish died

) he's going back home.
Rex, I think it will be fine to try this. You said you were concerned that your betta and the new one might flare at each other through the partition - they probably will, especially initially but it very well could calm down after some time. They can't physically hurt each other if one is enclosed. Someone said he might jump out - depends on your trap - I know mine has a lid, and if yours doesn't, its not hard to make something that will do to keep him in.
IMO, the best thing to do would be try it, but if after a few days they're both still going bonkers, keep the bowl on hand and then you can always just put him back.