OK, good. Get water out of the main tank and put it in the 6 gallon. Don't worry about a heater, betta's are ok without a heater for a while, and even if it does get cold then just add some hot water from the tap.
As for a filter, be ready to do loads of water changes.
I would say that this tank should be the betta's new home, because even if he gets better, then the Ram will nip him, so you may be better to go and get a pump for the undergravel filter.
Do you have any melafix in, or a similar product?? I would use this to relieve stress and fix any torn fins etc. Try and give him some food and see if he takes it... feeding him and giving him a tank to himself should perk him up... unless he has an illness.