So sorry for your (and everyone's) loss.
In my preschool teaching experience, when it comes to furry, rodentlike critters, hamsters appear to be the tricky ones; they seem to be rather delicate. I agree that a chill might well have done him in.
Also, I get the impression that hamsters do not always do all that well with kids and handling. Guinea pigs or <shudder> pet rats seem to take this sort of thing better.
Having said all that, I did have a guinea pig squeezed to death by a youngster, though the pet was indeed 5 years old, rather aged.
And the scatterbrained kindergarten teacher across the hall taught far too many death units as various pet rats succombed to the attentions of her students.
After all this, I got one of those Grow-A-Frog tadpoles, and never sent it home on weekends like I used to with the guinea pig. Eight years later the frog is still alive and well, and to the relief of my husband, my brother and his family now have Froggy, back in Colorado.
