3000 Farads by itself isnt enough to go by. We'd also have to know the voltage rating. That would tell us how long we could charge it at say 1 ampere. If we charge it too long and the voltage exceeds the voltage rating, we blow up the cap and it becomes no good to us anymore except maybe for a one time use on the Fourth of July.
The specs sheets from their web site say 2.7 volts so I suspect they are using standard super cap tech.
Granted their biggest ones are 4000 F 2.7 volts with a discharge current rating of something like 4050 amps!
see data sheet:
3000F
Shelf life \ 500 hours with no voltage applied at 60°C \ Capacitance change : <30% of initially measured values
So sitting on a shelf @ 60°C for 500 hours the capacitance can change up to 30%
30% of 3000F is 900F
500 hrs = ~21 days.
When you think of a shelf, usually it's in a climate controlled warehouse or something, so probably won't be 140°F (60°C). But a shelf in a service van sitting in a parking lot in Texas could easily be 140°F.
140°F isn't all that hot as far as electronics are concerned.