I have an on-demand water heater that is adequate for the hot water needs of the house.

It provides plenty of hot water for shower use, etc. However, when filling a bath the hot water does not kick on and it comes out ice cold.

It seems to me that the only difference between the bath and shower is back pressure. Do I need to increase this somehow for the bath to get hot water? Any suggestions besides a cork with a hole in the middle?