No; they are not mechanical devices so only the electronics use power. When idling most SSDs use less than 1W and often in the range of 0.1W, while normal 7200rpm HDDs use about 6-8W and the Green drives about 4-6W.
When fully stressed, it may consume little over 1W, but still does not come close to anything regular 3.5" desktop drives consume.
SSDs should never need any cooling. It should also be safe to use them in extreme temperatures; unlike HDDs which are extremely susceptible to temperature changes and diminishes their lifespan.