Is it bad to take a keg from cold to room temp?

Wasn’t sure how to title this so thats what I came up with. LOL! Anyways, my issue is that I made an imperial nut brown and kegged and carbed it too soon. I think it will do much better with some more age on it, but it is already rolling in my keezer. I can taste it getting better every week, but it is going really slow. Do you think I can pull it from my keezer and leave it at my warmer basement temps without any ill effects? I figure it should be fine under CO2, but wanted to make sure. Will the warmer temp speed the ageing process up?

Not an issue to do this and yes, the cold temp is inhibiting the aging process and warming it a little will speed things up. One caveat is that the cold temp caused the yeast to settle out, so there may not be a lot of yeast-related aging going on at this point.

Will there still be enough viable yeast in the keg after they warm up a bit? Would it benefit to shake the keg up and get what sediment that is there into suspension?

It is not still fermenting still, it is aging. I think you will do the beer a disservice by getting all the yeast back into suspension