I heat my tub from a 205L tank, heated by either the Lister or a boiler, using a finned heat exchanger from a CH boiler. The HE is under a wooden duck board, held down with some slab cut to shape. This has worked well for a number of years. It raises the temp by about 1 degree an hour. the heat source has to run for less than an hour a day. Pumps etc are controlled from PIDs. Initial heat of the year is boosted with a heater from one of the inflatable tubs I got second hand run from the lister, this gets it up to temp in a day. We run at 37c with the 205 never over 60c, a bigger differential would, of course heat it quicker.
If you go for a tank I would suggest placing your tub on some polystyrene and lagging with bales.