Can a boat propel itself by heating water at the bow and cooling it at the stern?

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Ontophile
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Two questions

1) Say you had a small boat with no motor or paddles; no propulsive device save the one I'm about to describe: mounted on the boat's outer hull and submerged in the water, there is a water-heating-mechanism at the bow and a water-cooling-mechanism at the stern. Since heat makes water contract and the absence of heat makes water expand, would these heating- and cooling-mechanics propel the ship forward?
 
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Ontophile said:
Two questions

1) Say you had a small boat with no motor or paddles; no propulsive device save the one I'm about to describe: mounted on the boat's outer hull and submerged in the water, there is a water-heating-mechanism at the bow and a water-cooling-mechanism at the stern. Since heat makes water contract and the absence of heat makes water expand, would these heating- and cooling-mechanics propel the ship forward?

Liquid water does expand and contract at room temperature, but not by much.

My observation:

The cooling system on the boat is going to produce more waste heat than it removes from the water; if that waste heat is "dumped" back into the water near the stern, then the area around the stern is actually going to WARM up, not cool off.
 
Also remember that the change in water temperature is going to cause currents going down and up also.