Furnace continuously calls for heat

Something amiss in the wiring. Have you verified what each wire is and what it does? Is this two wire or three? And don't assume, if it is three, that you have the same colour at both ends of the wires. You may have, for example, white, red, and yellow at both ends -- but it's perfectly possible that somewhere in between somebody spliced them oddly, and that the colours at one end aren't the same as those at the other.

If you can post a few pictures of the wiring and controls we will try and help

On the + side at least you have heat.

just to be safe I would shut the boiler or furnace off at the service switch and see if the burner shuts off and then turn the power on to restart

Just to be sure you don't have an unsafe runaway condition