Actually, it's okay to not cup them in water changes. Healthy bettas should be able to take in the shock of ammonia-less water. :) It's also not just about the temperature, after 30 minutes of floating in the new home, you have to pour out 50% of the cup water and add in small drops of tank water to reduce shock. You have to add in tank water every 5-10 minutes.
Did you not do this, crowntail?
Over hundreds of bettas die in their small, dirty cups each day. Only you can help them live. Research and then save them, today!