High temperature and high humidity will degrade your seed quality quickly. Consider them the enemy!
Fluctuating temperatures and humidity levels are just as damaging.
Seeds can be frozen for longer storage.
Seed moisture must be below 9% to avoid the internal moisture from swelling when frozen and damaging the outer seed shell.
Test to see if moisture levels are low enough. As a general rule of thumb, dried seeds that break when pressure is applied, instead of bending in, are 9% moisture or lower.
Use airtight containers to store dried seeds. Baby food jars or small canning jars with rubber seals work well. You can cut gaskets from rubber inner tubes or similar material to fit larger jars for larger stocks. Vacuum sealers can also be used.
Unless you plan to plant the entire contents of your entire storage jar, (never a good idea to plant all your seed at once-if you loose that planting, you loose it all!) when you remove it from the freezer allow the jar to warm to room temperature before opening. This prevents condensation from forming on cold seeds and partially re-hydrating them.
Partially re-hydrated seeds may exceed the 9% moisture level and die when refrozen. Choose the smallest jars possible to avoid frequent openings and temperature fluctuations to keep the remaining seed in best condition.