I play bass in my little mancave in the basement. The room is unheated but has an electric heater/radiator. The temperature might change +/- 5 degrees celcius every day. Especially during winter when the weather is cold.
I rarely have to tune the bass. And when I do it’s only a little bit.
Is it unhealthy for the bass to be stored this way? (It has a 5-piece neck).
No, your bass is fine. Just tune it whenever you need to. If you ever experience buzzing strings when you fret, you will need to adjust the truss rod, which is simple and safe to do.
Yep mild indoor temperature swings will not harm your instrument at all.
My basses also lose tune from hanging them on a wall in my studio which was an out building before the reno that didn’t get much of an insulation upgrade.
I’ll often strap the bass on myself a few minutes before playing it, sometimes several minutes and it brings itself back into tune or very close.
Sometimes I don’t wait and tune it but then after one or two songs I’ll need to retune it, for me I usually wait 5 minutes, my wall can be -5c colder easily so it seems to be just how it goes.
If your a musician on the road it will see more temp fluctuation than that. Basses are pretty sturdy
If you’re growing weed then a consistent temperature / humidity is good. 
Otherwise for a solid body bass. It’s not a problem
If you’re growing weed, it is highly recommended that you should play your bass…highly.
Solid body instruments are pretty hearty. After all the trees the wood came from experienced much greater temperature extremes than a few degrees.
When I was in HS and our band was traveling all over Northern Wisconsin and the UP of Michigan in winter there were times when it was -20° below outside and we’d need to haul our gear in from the trailer it was stored in and set up to play a half hour later. It barely had a chance to warm up.
Nothing broke but staying in tune was a real challenge for an hour or so.
I went to high school in Janesville. My gigmobile was a '64 Volkswagen that drew its “heat” from the air-cooled engine. In the winter, that car never warmed up. More than once, the girl I had in the car with me had to try scraping the ice off of the inside of the windshield while I was driving with my window open and my head stuck out of it.
NOT recommended.
Yup, as I recall there were some damn cold winters back in the 60s. One year during January it never got above zero for 28 straight days. The “band car” was a '54 Chevy we tooled around in for fun but our manager drove a newer '67 Impala and that’s what pulled the trailer from gig to gig. No van, no “tour bus” …LOL.
I had a 59 CJ 5 Jeep back in the day, and the way the duct was routed what hot air there was was cooled off by the time it hit the windshield. I kept blankets in it and hung an ice scraper from the rear view mirror so I could keep the inside of the windshield clear while driving.
This was also the vehicle that had a lever so I could operate the windshield wipers manually; they operated off a vacuum line and if you went up a steep hill, they stopped. Inconvenient in the rain. And no synchros in the transmission. To call it quirky is an understatement.
No problem at all.
Also humidity should be more a concern than temperature overall.