If I have two fish tanks with one fish in each tank, do you think it would be good to switch the fish to different tanks now and then, for a change?

I have two Siamese fighting fish (a.k.a betta fish). One fish is in a one gallon tank with a filter and no heat. The other fish is in a five gallon tank with a filter and heater. I have had both fish and both tanks for about a month. If you think this question sounds naive, please forgive me, as I am new to the aquarium thing.

Do you think it would be a good thing to switch the fish into the opposite tanks now and then? I am really wondering because the fish in the heated, larger tank is more active, and I am wondering if the other fish might like to try that out for a while. I am considering getting a heater for the smaller tank, but in the meantime I was considering switching the fish for variety.