A trumpet is small and light enough to be an easy carry, but its valves are precision-fitted pistons that heat and rough handling can affect, and a case left in a hot car is genuinely worse for it than most instruments its size. Casing it properly and avoiding extreme heat covers the real risks.
Pro tip: A quick valve oil refresh right when you arrive at the new place, even if you oiled before the move, accounts for any oil that migrated during transport and gets the horn playing smoothly immediately.
Watch out: Never leave a trumpet in a hot car or truck for an extended time; high heat can break down valve oil and soften lacquer finish faster than normal use would.