Temp is only important during fermentation???

Im thinkin I need to do a swamp cooler for my next batch. My house stays warmer than what I need to ferment at nowadays.
So my plan is to use a large rubbermaid bin with water and ice packs for the duration.
But does it need to be at that same temp until I keg?
Or is it just for the 7-14 days of fermentation?
Also does the water have to cover the entire carboy? Or will it only chill the wort that is in contact (albeit thru the glass) with the cold water?
Thanks for any responses.

If you have the option, it's preferable to keep it temp controlled for its whole life, but the period of active fermentation is far and away the most important time.

So long as the water covers enough of the beer to keep the temperature constant, you don't need to worry about whether or not it covers every last square inch. The liquid inside the carboy will move around enough to ensure an even temperature. You don't get stratification of multiple temperatures inside a single liquid to any significant degree like that.

The water should at least be above the wort level inside the carboy for maximum cooling efficiency. It's not a must, but it definitely helps.

As for temps...you'll benefit from leaving the beer at the same temp until your keg, but it's not 100% necissary. As long as it's consistant during the main fermentation, you should be fine.

the temp only needs to be maintained through fermentation. 3-4 inches of water is all that is needed in the swamp cooler a tee shirt or towel should be draped over the fermenter with the ends in the water. The water will wick up the tee shirt and cool the fermenter through evaporation. to get a couple more degrees of cooling you can blow a fan over the fermenter.