If they are like mine, they run on 12v
power, come on when you turn them on, and turn off when you turn them off. They are designed to get warm, not hot. I've been out in 26 degree weather with them on with no tank issues.
I don't know how much they draw, but I ran them when hooked up to 30 amp 115v power. Last time it was that cold my city water hose froze up, so we had to run on tank water at night, hose thawed during the day and was hot damaged--I did not let it happen the next night, so I disconnected, drained and stored it safely inside in the afternoon.
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'The Silver HamShack' (2007 International 22FB CCD 75th Aniversary model)
Multiple Yaesu Radios inside and many antennae sprouting from roof, ProPride hitch
2012 shortbed crewcab 4x4 Toyota Taco TV with more antennae on it