What temperature water do Betta fish need?

There are a lot of things that need to be clarified.

1. How did the Betta lose it's fins - fight or disease?
2. What conditions is the Betta living in? Small glass bowl or a proper aquarium with a filter/heater?
3. What kind of food are you feeding it?
4. How are you maintaining the living space?

If you're keeping the fish in a small bowl and disease has struck, you're going to have little luck. These bowls, while can sustain life, are like little prisons. Nothing flourishes in a prison.

If the fish has been attacked and lost it's fins, you need to make sure the attacker is no longer in the tank. The stress from the initial attack usually kills the fish so if it's not dead already, you're lucky.

If there was disease, you need to make sure to treat the disease properly (including change the water on a regular basis, feeding properly (not over feeding), and medicating). Again, small bowls are nearly impossible to dose properly so good luck if you're keeping your fish in a small prison bowl.

Ideal situation for the Betta's fins to regrow (and stay beautiful) - a proper tank (no less than 5 gallons) with a filter and heater (kept to adequate temperature). You change the water weekly. There are NO fish that nip or attack the Betta in said tank. You feed the fish quality food.

With luck, it will take time to regrow the fins. Usually, regardless of conditions, small fish die when subjected to physical damage . they are small, their immune systems are not designed to deal with the associated infections, healing is slower in cold blooded animals.

My Experience: I have a 60 gallon planted tank (my third) that has plants growing and flowering out of the water. I've had 4 betta's since childhood so I've had experience with this and other labyrinth fish.