answer:The thing you want certainly does exist, and it’s called a “water heater”. Your landlord should supply one that works to supply an “adequate” amount of hot water. Reasonable people can differ about what is “adequate”, but “not enough to wet my ankles in a bathtub” is going to be at the extreme lower edge of any reasonable person’s idea of “adequate”. Any device such as what you’re suggesting, while possibly workable, is not normally commercially available (I don’t think you’ll pick this up at Home Depot), and is likely to be unsafe in several ways: plumbing leaks outside the tub, and electrical shock hazard (or fumes and venting from burning fuel, for another). Talk to the landlord pleasantly. Maybe he doesn’t know that his water heater is limed up or has an element burned out.