When it comes to storing things for a very long time, generally speaking, the colder the better. At a temperature below —40° F. or C, there is a minimal amount of biological activity. Also, a few humans have chosen to have their bodies deep frozen immediately upon being declared legally dead in the hope of being resurrected at some future time when their cause of death can be reversed. The problem of course is how to maintain a super-cold temperature reliably for hundreds of years in a temperate climate.
I have an answer for the problem of keeping seeds at the EarthArk, and animal bodies too, super cold even for thousands of years without having a perfectly operating technical society to maintain them. We could call it a deep-space refrigerator. Deep space is very cold and NASA has already considered having a capsule placed on the Moon deep in a polar crater where the sun never shines, where it would reach a very low temperature. Of course, it might cost billions of dollars to get a small capsule to that location, and additional billions to get it back to Earth. The chance of a catastrophic loss for this round-trip operation is high. Fortunately there is a cheap and safe way to create a super-cold refrigerator that would keep materials very cold for thousands of years for very little money.
At the top of Antarctica there is an area called Argus Dome at Lat/Long -80.367 77.352, where the altitude is over 13,000 feet and the sub-surface temperature is about —55° F. In addition to that low temperature, I have a plan where a container buried there could be made even colder. The project would be to build a large container which is exposed to the —100° F. winter temperatures and sealed closed during the summer months. That simple procedure would lower the year-around temperature to something approaching the winter cold. But, much lower temperatures could be achieved by visually exposing a black surface to deep space for the four Antarctic winter months. If this large container were insulated from the world for the rest of the year, the cold temperature achieved in winter would be maintained. A thick wall and floor of high quality insulation would protect a large heavy object from warming. The insulation is aided by the low air density at the high altitude. Much lower temperatures could be achieved in this refrigerator by exposing a black surface to visual deep space, which is only a few degrees above absolute zero temperatures. The black surface in the container would radiate infrared light into deep space and cool the contents of the container.
Once a year as winter approached the top door would be opened to let infrared light out, and once a year as spring approached the top door would be closed to keep the contents cooled. This closed door would be highly insulated too. An alternate way to transfer heat to the storage area would be to have it totally encapsulated and an external horizontal black radiator elevated to where the snow would be easily blown off, and a solid copper shaft to connecting the two to conduct the cold from the collector into the storage container, which could be protected from the weather by being buried. The collector panel would be fully insulated too, and the portion visually exposed to deep space would be covered with multiply insulated and appropriately transparent glass. If the conductor rods were designed to expand and disconnect whenever the container temperature was colder than the conducting rod temperature, this system would be totally passive.
Once in place the EarthArk temperatures can be maintained at —100° F. for thousands of years without any human maintenance.