Lithium Ion (Li-ion) | Rechargeable Batteries Canada
The lithium-ion battery life is long, and they will not form a memory if recharged before it dies completely, rather it is beneficial to do so. This is much different than a regular rechargeable battery. Letting lithium-ion batteries completely discharge too often or to let it sit uncharged for a long period of time will shorten it's overall lifespan. When storing them for a long period make sure they are charged to 50-60% and they shoudl be removed from the device they are meant to power.
Be skeptical of the "techs".
At any rate, I suspect something else is going on. The back of the battery will get warm to the touch when charging, particularly when on the wall charger and charging up from a low state. And the BlackBerry will get warm if it is accessing the network frequently over time. And, running a battery down routinely does shorten the life of the battery. But the BlackBerry should not be getting too hot to touch, if that is what is being called red hot.