I built one just like this, in the summer it's great but in the winter as you are worried it's hard to keep the ambient without a heated room. Since it is open it wont hold heat at all. I ended up having to get a oil filled heater to heat the room. Only way around not heating the room would be to make it with the front/back enclosed & only open on the small end, (if that makes any sense).

I also use 11" flexwatt & no it wont heat the cool side at all. I have it measured at 1ft long which covers about 1/3 the tub but, a few inches away from the flexwatt it's ambient temp.