You can store most seeds fine at room temperature, but storing them refrigerated (not frozen, with the exception of a few plants' seeds) makes them last longer, especially with short shelf-life ones, like helleborus, corydalis, etc.

I store mine in the crisper draw in the fridge, in separate plastic bags. I make sure the seeds are dry first so they do not mold. The only exception I make to that are whole berries that I know I'll be using that year -- the seeds are cold stratifying in the pulp until I use them so that's useful too.

This from "Growing and Propagating Wild Flowers" by Harry Phillips: "Viability is extended when the seeds are stored dry and cold...The seeds of Blazing Star (Lyatris spicata) remain viable in cold storage for at least six years...Refridgerator storage is important because to keeps seeds fresh for sowing, you must reduce the rate at which they respire , or 'breathe', and normal refridgerator temperatures are sufficient for this purpose."

A lot of people have success storing their seeds at room temp, but I keep mine in the fridge to be on the safe side.