It's difficult in our climate to guarantee that you can keep the small outdoor structure above 60F. I have a wood-framed
greenhouse with 4 mil plastic sheeting and it keeps the plants from freezing, but it won't keep the turmeric (which probably falls into that above 60F
class) going.
It's not every day that drops below 60 in the greenhouse, a lot of winter days it gets downright hot in there and I have to keep the door open to get some more ventilation. It's those clear, cold days after a front comes through when it drops into the 20s at night and the next day only gets up to 50 that are the worst. Then I am filling all the buckets I have and putting them in the greenhouse to increase the thermal mass.
If you want to keep your small structure above 60, I think you are going to have to have an additional heat source for those times. If you put a 30 or 50 gallon fish tank inside the structure and have
heaters in it that keep the
water at 75F, then maybe the air temperature inside will stay above 60.