I want to know in the form of watts. I think time and power are
direcly dependant on each other.  I need to melt a 8" hole in the ice.
where: lake in MN, when: middle of winter. Ice thickness 15" I don't
know the ice temp it must change as you go through the ice.  Outside
temp 5 Degrees F. It can have a core to reduce energy needed. Purpose
to find out if I can melt holes in the ice with useing a large lead
acid battery 12 volts.  Please keep in mind the water will be preasent
which will conduct alot of the heat.  I have melted some holes in ice
in a 5 gallon bucket with a 500watt heat and a 8" alum tube walls
1/16"thick  but seems to take alot of energy. If someone can help with
a real world envirment.

Would a chainsaw do better - if a rectangular hole is ok ?

The required energy depends on how much ice you melt.  If you are
melting a follow cylinder instead of a solid one you get by with less
energy - hard to say how much exactly.   It could pay to make your
cutter insulated everywhere except the cutting edge.

I suppose someone lazy would put a removable (polystrene, cork ?) buoy
in the lake before it froze.

Bozo99, if you insulate the heated cutter so only the tip (or, say,
the first inch) is hot, you'd get refreeze after a few inches and the
whole thing gets locked in the ice.

Gocat, you're heating a hollow cylinder at least 15 inches long by 8
inches across. That's two surfaces that are 15x25 (let's call it two
surfaces of 400 square inches each) to a temperature of, say, 120
degrees F. That alone is a lot of power.

But when you have to overcome the energy of the state change from ice
to water... well, that's where the real power is needed. I'm not gonna
do the math-- I'll leave that to Google Researcher-- but one car
battery isn't gonna do it.

Cool experiment: put a block of ice as a bridge between two sawhorses.
Suspend a moderate weight (one or two pounds is okay) on a string
looped over the ice. Sprinkle a couple of pinches of salt on the
length of the string on the ice. Wait. In a few hours the string and
weight will have cut through the ice block and fallen to the ground...
but the block will be whole. It refroze behind the string!

Let's suppose you wish to melt a cylinder of ice that is 8" in
diameter, 15" thick, and 1" wide. That is pi*8"*15"*1" = 377 in^3 or
6178 cm^3. The heat of fusion of water is 335 kilojoules per kilogram.
Ignoring the heat required to raise the temperature of the ice to
melting temperature and heat lost through conduction or radiation, the
total heat required is:

(335 kJ/kg)*(6.2 kg) = about 2 megajoules

at 500 Watts (Joules/sec), it would take 4000 seconds or about one
hour to melt this cylinder. It is more work to estimate how much heat
would be conducted away, but this will increase the time required.

A typical car battery holds about 100 amp-hours at 12 volts or 1200
Watt-hours, about the right amount of power to melt your hole.

Oops! I meant to say that a car battery holds about the right amount
of ENERGY (not power) to melt your hole.

Yeah, but you can't forget the heat needed to raise the temperature of
the ice to 32°F.  Gocatgo is assuming the outside temperature is 5°F. 
At that temperature, I don't think that salt is going to have much
effect.  I expect that if this could be done, someone would be
marketing it, but it seems that power augers are what is available:
http://www.strikemaster.com/power.html

OK, we can add the heat required to raise the temperature. I didn't
include it because this whole calculation is just a rough estimate and
it is small compared to the heat of fusion:

4200 J/kg/K * 6.2 kg * (32 - 5)F * 5/9 K/F = 0.39 MJ

Add that to the approximately 2 MJ and you have 2.4 MJ.

A bigger effect that I don't intend to calculate is the loss of heat
due to conduction, radiation, and convection. Let's assume that you
melt the ice instantaneously, so this contribution can be ignored.

The conclusion is still that a 100 Amp-Hour battery is big enough, but just barely.

I thought it was a stupid idea had to try I did insulate the cutting
edge there was so much heat conduction still  the water would never
freeze but was still a very slow process bought parts from mcmaster. 
I was worth a try.

What about ultrasonic