Wow! Very diverse opinions on this subject...
I have a rinnai tankless water heater in my home. No problems with temperature regulation - it has a modulating burner that monitors outgoing temp and ramps up as necessary to maintain 120 F with increasing flow.
And yes - it has a 125,000 btu burner, but, it only fires when hot water is used. No standby losses like a tank model. There is plenty of evidence that tankless water heaters save propane... Personally I estimate 30% less propane used!
I've been waiting until I need a New heater - I plan to install a tankless unit in the TT!