Cold Water in Bathtub

I recently moved into a new house and have noticed a problem with the water in the bathtub. My wife and I take a shower everyday and have plenty of hot water; however, when we give our daughter a bath we can never get hot water. In fact, most of the time it's luke warm to cold. The fixture has one handle with a lever to switch from bathtub to shower. My guess is that these's some part inside the fixture that needs adjusting/replacing. I'm pretty handy but I don't want to take anything apart without some direction.

I should mention that the hot water is heated through my oil fired boiler and that we don't have any hot water problems elsewhere in the house.

Thanks for your help.

The problem is in the mixer valve. Either repair it or replace it. Likely cheaper to repair, easier/quicker to replace.

Thanks for your help. It sounds like I need to make friends with the plumber next door.