I don't think there is any hard and fast rule about water temps causing Crappie to seek deep water. I do think that, in Summer and Winter, they are more prone to being in deeper water ... and move vertically in the water column - while in Spring & Fall, they are more prone to being in shallower water, and move more horizontally. Even that isn't always the case.
They're cold blooded, and as such will seek out the most comfortable water temps available ... but, can survive a wide range of temps (a little over freezing, to the 90's degree range). It's their metabolism that's mostly affected by water temps. And one thing's for sure ... they gotta eat - so they will position themselves in the water column, wherever there's baitfish ... and typically wherever there's some cover close by (either below them, or in the same depth range).
Different regions of the US, and even different lakes in any one state, are different in some, to many ways. The fish, in those waters, may be in totally different depths ... in the same time frame/season. The layout of the lake, it's mean depth, cover type and availability, water color, depth fluctuations, and general weather conditions will dictate where the productive areas/depths are. But, if your waters have a thermocline (and don't "turn over"), they won't be below it.
They can't read a calendar,or a thermometer ... they simply use survival instincts, and make the best of the situation they're in. It drives their feeding habits, breeding habits, and travel plans. Water temps are just part of the equation, and it impacts the food source's location & depth. Locate the baitfish - locate the closest cover (ambush point) - and you'll have a starting point ... then, expect the Crappie to be on a level with them, or slightly below them. ............ luck2ya ......cp
(I could be way off base, here ... so, if I am, please feel free to correct me - especially you guides, and anyone else that fishes frequently and/or year around)