Water is densest at 4 degrees Celsius, but it’s not that much denser than water at other temperatures. Exploiting tiny differences in the density of water of different temperatures would be a very inefficient way of producing power. 
The only ways I know of that produce significant amounts of power from cold water are hydroelectric power (dams), tidal power, wave power, and power from ocean currents (analogous to wind power). Each of these involves falling water or water that is moving somewhat rapidly.