A picture would do wonders to help us understand what your trim is, what your trim is like. Define your "trim" better, than what you have. Is the trim made of cedar, also?
Most cedar chests are lined with ER Cedar and the outside is usually made of a different wood. Your chest may be all cedar.
Is your trim long strips along the edges/corners or is your trim a carved or decoartive applique? The fix may be/ could be/would be different for each application.?!
Cedar chests are usually made of air dried lumber, not kiln dried, in order to have the effect of the aromatics of the cedar. Previously kiln dried lumber, for the trim, would/should not be warping, as the wood would have been "worked", to eliminate the possibility of warping, before it was applied to the chest... at least that's how I would have built it. This rationalle allows the conclusion that your wood is air dried.
From your initial description, I am assuming your trim is long strips, and not a decorative applique of some sort.
If your trim are long strips, along the edges or such, how thick is the trim? Before attempting to clamp down the trim, to possibly straighten it, you might try removing the affected trim and rip a kerf (or 2) along the back side, if the trim is thick enough to allow for a kerf cut. If so, don't rip the kerf all the way to the ends of the trim... stop short of the ends. This kerf cutting may break the tension, in the wood, and allow it to better sit flush onto its application.
Kerf cutting can be a delicate matter, depending on how thick the strip is.
If you use a router, a small "V" cutting bit works well.