Hmmm. I stopped storing stuff in my trunk, because I figured the extreme heat would eventually damage the plastic containers. My car is under the Hawaiian sun 24/7. I've had a break in my duffel before, (fortunately it was
upholstery cleaner). But I never blamed the bag, I blamed my own laziness to leave it where it'd break easily.
Now I take the bag out of my car and leave it under the stairs. Someday, I'll invest in a storage container with shelving. But this works for now. But go with the tub idea. Cheap and modular for easy storage.