First, good job on being an awesome person to save bettas from your local pet store (LPS). However, you have to have proper setups for the bettas to be happy, healthy, and well taken care of. What you could do since you like to rescue bettas. Once the bettas get back to great health and look good then give them to someone who will give the betta a good home.
I agree with the others that you do need heaters for each tank unless you keep your room in the 80s or 90s. Think of it this way: the temperature of the water is 20 degrees lower than the temperature in your room. Bettas survive happy and healthy in 72 degrees to 80 degree water. The colder the water the more they are able to get sick.
You should not have 2 bettas in a divided 2.5 gallon tank. You can do 2 bettas in a divided 5 gallon tank. That would be better temporarily. I have my 6 bettas in 2 10 gallon tanks (divided in half so 2 bettas in each tank), 1 2gallon tank, and i have my rescue in a 1.5 gallon tank by himself. He is only there short term as I am looking for a home for him.
How many 2.5 gallon tanks do you have? You do need a filter but not with the current setup you have right now.
America (f, HM), Spirit (m, DBLT), Rescue (f, VT), Missile (m, HM), Purnurple (m, HMPK), Dragon (m, VT), platies, mollies, sorority tank of 21 females, AND lots of guppies.