I was laughing out loud when I read about the ice cream thing. xD
My guess is the reason why he was flaring at the bowl(or ice cream?) was the reflection. I wouldn't worry to much about that though, unless he's flaring all the time, which would mean he's over-stressed and such...
About the 'dropping/nose dive' behavior, that's probably not a problem since someone that had experience with that sort of thing said that's normal. However, staying at the bottom of the tank and not moving would mean the water is too cold. Or staying at bottom of the tank, motionless with gills moving rapidly would also be a concern(ammonia or chlorine poisoning from what I've heard on this site).
I know that when warm water is poured into a betta fish's tank/bowl which the water tempeture is colder than the water being poured in, the reaction would be the fish kind of 'twitching' and then freezing, or seizing up and slowly dropping to the bottom. Afterward, the fish gets used to the rapidly changed water temperature and is OK. Usually. That's what happened to my friend's fish and it's alright, though that's probably not the best thing to do...:l It doesn't sound like you're doing that though so I'm sure everything's OK.
Since you can't get a heater for now, maybe you should get one of those 'floating thermometers' with those suction cup thingys, so the temperature can be monitored. Most should cost around two or three dollars.