The ultracapacitors can be stored in a fully discharged state. This does not affect the internal chemistry, lifetime, or future performance of the ultracaps.
They are best stored in a discharged state so they do not experience any voltage which can possibly decrease the lifetime (if at maximum voltage). When an ultracapacitor is in a discharged state there is no affect on the internal chemistry of the capacitor, where as in a battery it will experience coagulation. Storing ultracapacitors at low or 0 volts has no negative effect on the capacitor.
Storing the capacitors while charged, although not ideal for lifetime, is fine as well. Since capacitors do have leakage currents, they will slowly discharge and eventually will reach a very minimal voltage, which is the best way to store them.
The leakage current does vary with temperature, and you can visit What are the expected leakage currents at various temperatures? to see how the currents change with temperature.