Immersion query

We have a tank in the airing cupboard and an electric shower. We normally only switch the water on when we have a bath, and for the past few weeks with the hot weather, have only been having showers. So the water hasn’t been on. However, some of the pipes in the airing cupboard are hot, and we still have hot water coming out the kitchen/bathroom taps. As far as I am aware, the immersion heater isn’t on (although I’m not sure where this switch is) but all switches in the airing cupboard have been in the off position for a few weeks now. So, I can’t understand why some pipes are still hot, and we still have hot water coming out of the taps. The boiler doesn’t fire up (like when we put the water on and we can hear it). I am trying to keep costs down, so am concerned as to what is going on, if anyone can help please?