Since it's a 2.5-gallon you can't really cycle it and need to do 100% water changes so cycling isn't the issue. Actually, cycling such a small tank can be dangerous.
Temperature probably wouldn't have caused such a quick death either. But when you said he heated the water first does that mean he put in warm water or used an actual heater?
If the tank is a Mini-Bow tell him to take the filter out because they are too strong for bettas and will bother the shrimp, too. In a small tank for a betta you do not need a filter.
Was the water dechlorinated? And that doesn't mean leaving it out overnight. Maybe he forgot water conditioner? If not, maybe your town uses chloromines and his dechlorinator doesn't remove those?
The water should be tested in case the pH is really off or something. Though I doubt that's the problem.
But there's a good chance he did nothing wrong. Sadly, many bettas are unhealthy when purchased
. Remember, they are often shipped from Asia and are kept in very small containers. Several don't even make the trip.