Erik describes the cold crashing process well. Just to reinforce, no, you don't have to warm it up to bottle. Priming calculators take into account the amount CO2 already in the beer when they calculate the total CO2 for carbonation. You base the amount of priming sugar on the warmest temperature post-fermentation. So if you fermented at 64F and then raised it to 68F to finish up and reach FG and then let it sit for a while longer at 64F and THEN cold crashed, you would prime based on 68F regardless of the temp at bottling time.
This is because fully fermented beer will off-gas CO2 as it warms. As long as fermentation has finished (i.e. FG is reached), when the beer is cooled it will not regain any of the CO2 that was off-gassed or create any new CO2 by fermentation.
Now just to be clear, if we use the same scenario (64->68->64->33) but you didn't reach FG until a few days after you dropped back to 64F, you would use 64F as your temp for the priming calculator. It's all about the highest temp after fermentation stops.