To put some rough numbers to what Hampshire said:
Skin and fat have a thermal conductivity of about 0.2 W/m/K. (For reference, water is about 0.6 W/m/K.) The surface area of a human is about 1.5 m[sup]2[/sup]. Now sit in a bath. Say the separation between the bath water and your body’s 37-degree-C core is about 1 cm. Then,
2 C[sup]o[/sup] difference ==> (0.2 W/m/K)(2 K)(1.5 m[sup]2[/sup])/(0.01 m) = 60 W
10 C[sup]o[/sup] difference ==> 5 times higher than above = 300 W
Under normal conditions, a human outputs about 90 W of heat. So, a 35 degree C bath feels refreshingly cool (helping you get rid of 60 W out of the 90 W you have to get rid of). A 27 degree C bath, though, is sucking out your very soul.
A hot bath at 39 [sup]o[/sup]C (or 102 [sup]o[/sup]F) is a little different in that you need to absorb 60 W of heat. That’s not too bad, though, adding as much internal heat as you would by, say, jogging.