It is not very difficult to make a heating coil for water.
We can make these to use water as a transfer element for heating, essentially the same thing here only you are heating milk instead of room air.
What you need is some good copper pipe run into a coil, the coil sets just off of a transfer plate (a steel plate) which is heated by any heat source you wish -gas, electric, wood, whatever. The water runs into the middle of the coil, and out of the end.
Such a system will actually create convection if done properly, so no pump is needed. But you might want a pump if you can't figure out the proper setup. Convection works because the water will have variable pressure in different temperature ranges, so if oriented properly the vat will actually actively draw the hot water away from the coil, in the mean time pushing the cold water into it. But if you want total control, you need a circulating pump (otherwise you have only indirect control of heating rate by adjusting burner temperature)
It is very important to have regulator valves and emergency release valves so that the water will not boil and explode. The regulator valves will maintain the water at a constant pressure -otherwise it turns into steam and exerts force on the pipe until the point of failure.
A well made system can run on low pressure steam, but you need to be sure that all of your pipes are properly fit.
Electricity is probably impractical for this situation. You can obtain a suitable propane or natural gas burner to do the trick or place a coil on the heating plate of a wood stove. But you do need a good deal of heat.