Watch out here.
Depends on the type of electric motor. Some will run on DC or AC. Some won't. So some are speed controllable and some are not - well perhaps better to say some can easily be controlled by voltage and some by frequency. Egs a simple mains electric drill motor with armature, commutator and brushes will run at the same speed on a similar DC supply, but an electric clock motor requires frequency for constant running speed (they keep 'perfect' time only if the supply freqency averages exactly 50Hz). Of course mains AC and equivalent DC motors are normally designed slightly differently to each other, but that is another matter and to do with high voltage DC supplies.
In terms of electricity use, if the low voltage fan is supplied with a power supply, mounting that somewhere inside the warmer would utilise both any heat entailed with the power supply and the motor -and would supply a small background heating supply of somewhat less than the heat being lost through the insulation. 'Waterproofness' needs to be addressed, of course.
Only waterproof mains electricity connections should be used below any level up to which honey might fill, should the container fail.
Most vivarium controllers only have a range to about 35 degrees Celsius - not enough to completely liquidise OSR, and any other honey in a reasonable timescale. Partial liquidising is no good at all if the honey is to be fine filtered.
So more thought needs to go into a honey warmer than perhaps meets the cursory glance.
MM's voltage controller is somewhat less efficient than newer controllers and the same goes for simple supplies. Older power supplies are really current gobblers and there is a system now to rate them from (roman numerals) one to five.
When we changed our phone and ansafone we reduced our power supply running costs by between ten and fifteen pounds a year. Not bad when the whole new system (better than the old one) was sourced for only a tenner - an unused/unwanted item at a car boot sale.
RAB