I wonder how concerned I have to be about a temperature drop of my bassoon.
As an example, after visiting my music school, the instrument stays in the car for another 2 hours.
After that, the bassoon doesn't have to be played on until the next day.
Is that "unhealthy" for the bassoon when it becomes cold?
Should I take it with me instead of leaving it in the car?
Greetings,
Willy

Where do you live? If it drops to freezing at night you might need to worry a bit, but generally bassoons are hardy animals and don't crack like the more thin-skinned oboes. Personally, however, I still would try to bring the horn indoors rather than leaving it out in the car overnight, just because the temperature you live in doesn't fluctuate as much as the outside air. It's not the temperature actually, it's the fluctuation, as you suggested, but still, why take a chance?

Thanks for the advice!
I live in Belgium. We have what is called a moderate climate, meaning a lot of not so nice weather.
Freezing temperatures don't occur very often. The reason I don't take the bassoon insde all the time is that it is easier
to just leave it in the car :-) After music school, I do sport and so I already have to take my sprotsbag with me.
But I will follow your advice and take the bassoon inside when it freezes.
Greetings,
Willy

I agree with Drew's comment. It's best not to leave it where there are real extremes of temperature but a few degrees below zero shouldn't be a problem. I suggest leaving the bassoon to get slowly up to room temperature before playing it.
More damage can be done by leaving instruments in cars in hot weather. For one thing the glue holding the pads in can melt!

Since the case is padded, it may slow down the warming up or cooling down of the bassoon.
I will take care not to leave the bassoon in the car on hot days, good advice!
Greetings,
Willy