There are a couple of bits of thermodynamics to consider.
[1] ICE is solid water [look here at the wiki on melting](https://en.wikipedia.org/wiki/Melting)
so if my thermos is full of a half frozen drink (or water with ice cubes) there is a huge amount of energy that needs to transfer into my drink just to make it all liquid at 0 C .
[2] Temperature differential.
a drink at 0 degrees is only 20 degrees from room temperature
my tea (made with boiling water) is ideally 100 degrees, and 80 degrees above room temperature.
The temperature differential between my drink and room temperature is the primary determinant in the rate of change in temperature (the drink approaching room temperature).
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