I should think that the hossie would be heated & the temerature quite regulated so you shouldn't have to worry too much?

Personally I wouldn't be too worried, if you're cold just let someone know & you'll be sorted, but I think with the hot water of the shower & the bath, combined with your exhertion, being cold will be the least of your worries!!

I had DP applying ice water to my forehead when I was in the bath!