If you put your priming solution in the bottling bucket first then rack on top of that, the swirling motion will mix the wort/beer and solution, so priming cold wont matter. Some will mix lightly too without incorporating air. I don't know that this is necessary since the solution is heavier than the beer and 5 gallons will dilute and fully incorporate that small quantity of solution. But hey, stirring is cheap insurance!
As LAKing mentioned, crashing is typically used for kegging. Often it is not done as the beer will clear upon refrigeration. Plus, the residual yeast will allow it to more readily carb. The only drawback to this method is more sediment in the bottom. But after aging/conditioning it will be hard packed (or should be) and will be of no worry.
On Deck: Cream Ale and Blue Moon clone for MIL
Primary: Hopped Up Brown
Bottled: Litehaus Wheat, Orange APA, Rauchbier, Willy's Cream Stout
Kegged: Tank 7 Clone renamed "Le Ferme" (dryhopped cascade, sorachi), Caramel Amber Ale, Trout Bum APA, 3 Dogs APA
Gallons Brewed Since June: 53.5
I seriously cannot imagine a day or life without beer!