Alright Mr. Clark - let's think about heat transfer for a bit here...
let's pretend there is no mixing in the ocean and that everything is
perfectly calm during a hurricane (excellent assumptions no?). Alright
now we have a 1 cm think layer of water at 20C and the rest of the
depth at 25C (compared to the 1 cm that is 20C, the amount of water
below it at 25C might as well be infinite for this little exercise).
I will assume no heat is transferred from air to water (another
excellent and good assumption!). Let's see how fast we lose this
critical temperature difference.

The temperature at the surface of the ocean is the most critical so we
can think of this cool layer as trying to maintain 20C at the surface
of the ocean. Therefore, the DeltaT is 5C, the difference in T between
the bulk ocean and the surface.

The thermal conductivity of water is roughly 0.6J/(s-m-C). The
thickness of the layer is Delta-x = 0.01m. We will consider this
problem using unit area of 1m^2 (we will assume this is an infinite
plane of cool water, a reasonable assumption for an area somewhere not
at the edge of your cooled ocean area).

The heat flux is given by Q = (k/Delta-x)*A*DeltaT = (0.6/0.01)*1*5 =
300 J/s. (you can check it yourself, the units work out propoerly - i
was lazy and didnt want to type them again).

Alright so we have heat flowing at 300 J/s. As the temperature
difference drops (i.e. the temp of the surface rises), Q also drops
linearly with the drop in DeltaT. Let us use 150 J/s as an average
over a large part of this temperature rise at the surface.

The amount of heat it takes to raise the temp of that water by 5C is
given by (specific heat)*(mass)*(deltaT)

energy needed = 4.19 J/(g-C)*(.01m*1m^2*1000000g/m^3)*(5C) = 209500 J

Now at 150 J/s this says our water will be roughly heated in 209500/150
s =~ 1400 s =~ 23.5 min.

So you will loose your deltaT in less than 25 min assuming perfectly
calm water, no heat transfer through the air, no mixing in the water,
and my crazy simple model that assumes your 1 cm heats identically all
the way through (as the water in that 1 cm layer heats, the surface
will heat more and more rapidly as the water near it warms - and finite
element model [or finite difference] here would help alot). Lets think
about a hurricane for a moment he huge waves, extremely turbulent
water, high winds whipped the water around - the mixing in the water
itself would kill your cool layer in a matter of seconds (when you put
ice cubes in a container with water and shake it around, you will melt
the ice faster than if you take that same volume of water, put the same
amount of ice in it and heat it over a flame). I'd say plan on cooling
down to a rather deeper depth than 1 cm - like maybe a couple hundred
feet and pray that they are no currents down there to sweep your cool
water a couple hundred miles away.

Let me know how it goes - and don't kill ALL the fish if you help it.
And give me a heads up - if we are going to do this, let me set up my
ammonium nitrate plant!