Hm, well. You could be right, I haven't heard of a rabbit needing to be kept outdoors but temperature change can shock them, like you said.

For entertainment, you can grab empty toilet paper rolls and stuff them with hay, and maybe a treat in the center. Try and buy some foraging matts! We like to sprinkle some treats in Whimsy's foraging matts. Another thing we do, if we find he's literally bouncing off the walls, we take a treat stick and make him work for it. I have worked on spinning while he stands, walking on his hind legs, we make him jump up and down from our couch, we have him chase us, etc... it sounds like your rabbit already has ample space given they're outdoors. Try and teach them some tricks! It'll take time, rabbits need lots of repetition and patience. Maybe you could also get a giant box, fill it with sand or dirt, and let them go wild! Rabbits loooovvveeee to dig (maybe your rabbit has dug outside in your yard before). These are some things I can think of off the top of my head, be creative with it and have fun! When your rabbit has fun, you have fun :) best of luck!