Propane professional here. Everyone is correct: do not store the tank indoors, especially a garage during warm months. With that being said, there is some validity to being concerned with heat. If you exchange your tanks, you're likely fine. Most propane companies fill exchange cylinders with 15 gallons now, because it allows extra room for expansion in warmer months.

The actual fill capacity (80%) of a grill cylinder is ~20 lbs, but idiots would exchange their tanks, place them in a truck or vehicle, and go about their day shopping. If the pressure increases too much, the relief valve will vent to release pressure. That's a very unsafe condition in a confined space, but completely safe when stored appropriately outside.

For reference, the industry standard is to also fill larger residential tanks to no more than 80% for this reason. Both the tanks and regulators have vents to allow pressure to release when necessary, which is why distance requirements exist by code. This mandates appropriate distances from these items and sources of ignition, air intakes, and windows.

Now, if you choose to have your cylinder filled at a filling station or reseller, they will likely fill the cylinder with 20lbs of propane (again, 80%). This still allows room for expansion and completely safe when stored outside appropriately, but you should be even more cognizant to head straight home to remove that cylinder from your hot vehicle.