Water is an excellent heat transport fluid, due in part to its high specific heat. The problem is getting heat into and out of the fluid - which requires heat exchangers with relatively high surface area. At the molecular level, heat is kinetic energy - movement of thermally excited molecules. Transferring kinetic energy from one molecule to a distant molecule requires collisions and momentum transfer from molecule to molecule, which takes some time. Also in a fluid, the molecules are free to move which gives rise to convection currents, but that is a slow way to move heat energy. Contrast this with a solid bar of a good heat conductor such as silver - the molecules are not free to circulate and they efficiently transfer energy in the form of vibrations to their neighbors.
Cletus has a good answer, who in the heck told you this? Water is an excellent conductor of heat. The fact that it's specific heat is relatively high is one of the things that make it a good conductor of heat. Now a little technical detail... Heat flows in 3 ways: convection, conduction, and radiation. Water (as liquid and as vapor) is really good at convecting. Water is also fairly transparent so it allows a good deal of radiation. As far as conduction, liquids and gases that convect easily do not need to rely on conduction very much, so, in terms of heat transfer, conduction is not very important. In fact, I'm not sure how you would measure the conduction of liquid or gaseous water, separating the conduction component from the convection would be very difficult. Solids are, as you might expect, not very good at convecting so, in solids, conduction is typically more important than convection.
Says who? If water is such a thermodynamic outcast why is it used in every power generating plant in the world?
The specific heat is too high.
