Feeling The Heat

The only photo I took today, leading to another question re central heating.

We switched the father-in-law's storage heaters on when we visited him earlier in the day. Later we got a call from him, worried that they were getting too hot. I don't really 100% understand how they work, regarding when/how they take heat in and when/how they give it out, but I do know they are supposed to get hot. But can they get too hot??

While we were there we managed to get him a flu jab. His surgery has plenty of over 65's vaccine, but have run out of under 65's, the opposite to the situation with my GP. What is going on here?