Will audio gear be ok in unheated house

I'm not suggesting a toy heater.

entire homes have electric baseboard heat, they are left on low for winters all over the world, Countless people from the North East go to Florida for the winters

quickie search, this one is plug, or approved for hard wire

a thourough search will find many safe options

all you need is a closet with an old school incandescent light bulb in it, left on should be enough to keep the closet warm ie above freezing and dry. And not run up your power bill. 

Marine supply stores offer low wattage heater sticks expressly for dehumidification. They're not expensive and far safer than a room heater or light bulb. I'd also consider making the closet more theft-resitant with a heavy duty door, hinges, and lock. At a minimum, line the inside of the door with 3/4" plywood and install a deadbolt. It won't stop a determined thief, but it will slow and hopefully discourage them. Look

@glennewdick ....with some simple insulation and a fresh bulb, your concept ought to fly nicely....the only fly in that soup would be an extended power outage....but with desiccant.in that space as well, ought to be as safe and sound as possible..👍.

@dill

"when I leave in the fall for theft worries"

- So you are changing your mind about this reason?

Your quote left off most of the original sentence.

It said:

when I leave in the fall for theft worries, but mostly because I am not sure the equipment will be OK in an unheated house in an often damp environment until the late spring when I return.

Theft worries are not the primary reason for moving the equipment.