It requires 1 btu (British thermal unit) to raise or lower 1 lb of pure water 1�F at sea level. That is called sensible heat.
It requires 144 btu to change the state of 1 lb of 32�F liquid pure water to 32�F solid ice at sea level. That is called latent heat of fusion.
To change the temperature of 1 lb of 212�F water to 32�F water requires the extraction of 180 btu. To change the state of that 1 lb 32�F water to 32�F ice requires a further extraction of 144 btu.
So you're simply talking about the extraction rate of btu (heat) from the water. The greater the temperature difference the faster the transfer rate.
Let's say you have #1 liquid at 200�F and #2 liquid at 100�F. After 10 minutes the 200�F #1 liquid cools to 100�F (-100 btu) while the 100�F #2 liquid only cools to 60�F (-40 btu).
Now #1 is 100�F and has the same transfer rate as #2 did (-40 btu) over the next 10 minutes while heat continues to be extracted from #2. So you can see that #1 can never catch up with #2.
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