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Termperature conversion conundrum.

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   This is a word problem, I think.  I know I'm doing something wrong along the lines of the bellboy's missing dollar but I don't know where I'm messing up. Could be my physics, or maybe even my gozintas. Can someone help me?     Here 'tis:

      Latent Heat of Fusion ice stated in layman's terms says the following take any quantity of ice, I'll use an ice cube at exactly 0oC and apply exactly enough heat to melt it and you end up with water at 0C. All the energy goes into breaking the molecular bonds and no heat at all is imparted to the substance. Now, if you apply the exact same amount of energy to that 0C water the water will absorb enough heat to raise it 80C. With a thermometer it will read 80C. 80C is 176F. Pretty dang hot. You can even use a thermometer to verify it 80C

   Now keep in mind that 80C=176F

  Let's do the same experiment with the Fahrenheit scale. Apply the heat to a 32F ice cube and you get 32f water. Now you pump that  same amount  worth of additional heat into that water, added heat,  and the temperature goes up, increases, by 176F.  equals the 80CCelsius experiment.

  Here's my problem The F scale at which this experiment begins, the temperature at which the frozen ice cube begins it's journey, is already at 32F. If the additional 176 degree rise is added on to that we get 208F which is 98C.  Where did the extra 18C come from, or conversely, where did the 0riginal 32F run off to?  I haven't performed the experiment so I really don't know what I will end up with.  I would imagine the water is at 80C. But. . .

     What am I doing wrong?

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