Do you turn off a natural gas furnace in the summer?

[Virginia Jones]

One of our rentals has hot water heat powered by a natural gas furnace. The furnace has an automatic pilot light so it doesn't have a flame that needs to be lit. Would you leave it on in the months when it's not being used or turn it off during the summer? If it doesn't hurt it at all I would rather leave it on so as not to have the tenant messing with it and I won't have to go there to turn it on and off.