I think that as long as things don't get under 55 degrees they should be allright. But you may have to do a test run and see how cold it gets in your particular setup. Hopefully some more people will comment and throw out some ideas too. But what I think is that you'll have to test things out and see how it goes and adjust, but be ready to make the adjustments, like adding a heater/thermostat if things turn out to be too cold. I hope this helped some, but if not ask some more, maybe I, or someone else can help.
How far is your shed from the house? If it's close,within 100' then if you are able get a wireless weather station and monitor your temps doing a trial run without plants.
That way you can do tests without killing your plants due to a surprise of some sorts. Once you have your heating issue resolved then start your grow in the shed. Here's a link to site that has the weather stations.
I wonldnt do it with out humidity control,water bottels?Are you serious,Id seriously think about it first.
One of those genorators Hazy gave you a link would help control the enviournment and increase your yeilds.
Not that expensive for what it does.
You dont want to loose a crop too mould!
How about a kerosene space heater or a small propane heater/CO2 generator. If you were to get a small CO2 gen you could probably run it during lights on also. At least in the winter you could.
WORD!They have neat little top up systems,handy for going on hols,or for the piece of mind.
Its normal to top up in the heat,just take into account the evaporation when feeding.Goodluck!
I've heard feeding yer plants seaweed can make them more resistant to cold/frost. We had no problem last year in our shed, just using the light for heat.