Prevent Frozen Washer Machines

[Sunny Burns]

So we built a laundry room in an Unheated portion of the building... I live in NJ where we do have abundant below freezing days. 

I did just finish installing heat cable on the cold and hot water running from the house to the laundry room. 

But I'm concerned that won't be enough and the water that's trapped in the washer machine will expand and break the washer machine. Does that happen? I think the pipes will be fine with the what cable, just worried about the washer machine itself. 

If so have to I guess I will install an electric space heater and keep it on low.... any thoughts?