We leave our summerhouse door open all the time, now we've a catflap I'm still doing it as the neighbours cats hang out there when it rains!
They are pretty smart at finding themselves somewhere sheltered to hide. My hunter cat has stayed out all night a few times (pre cat flap) when I thought it freezing, but he's strolled in at breakfast seeming fine so probably slept in a hedge all night quite comfortably.
I would speak to the landlord. If you've got a double glazed back door for example with glass at the top and plastic at the bottom, then you can put a cat flap in and just replace the plastic when you leave very cheaply. The same goes for single glazed glass. And anyway I'm sure many landords wouldn't mind having a cat flap - it could be seen as a perk for future tenants.
Failing that I've got no idea.
I've just thought, if it's the idea of him being stuck outside in the cold/rain that bothers you, you could get him a cat kennel.
My Maine Coone boy has suddenly decided that he likes to be out, and often doesn't come in before we go to bed. I get worried about him especially when it's raining, and he recently had 2 nights out in the snow.
I'm too paranoid to leave a window open, and am in rented accom so can't put in a catflap. Does anyone know of contraptions for sale to use on double glazed windows?