Bathtub water heaters are used in air baths, whirlpools or combo massage tubs to maintain water temperature for longer periods of time. They are not meant to be used in standard bathtubs.
A bathtub water heater is designed to maintain the original temperature of water added to the tub for a longer period of time. Some may be able to maintain the starting temperature indefinitely while running. Each particular tub may require a proprietary brand made by the manufacturer.
These heaters are usually meant for maintaining the water's starting temperature and not additional heating. If a tub cannot get up to the desired temperature when full, the heater may not be large enough for it.