Running a computer in an unheated building?

I am thinking about trying to run an older via vtx system in a barn.

In New England, so outside temps might be down to -15F and probably not much better inside. It would be an always on, headless system - no monitor keyboard or mouse. Just a usb external wireless internet for connection back to servers.

What are the chances that the heat generated inside the box would keep the temperature up enough to operate hard drive etc. reliably?