A couple of easy tests you can do.
The typical temperature inside your fridge is 40f, the freezer should run at around 0
So depending on what you call cold, shove your insulated container or flask in your fridge /freezer, leave that for the desired time (IE I want my drink to be hot for 2/3/4/5 hours) and you will have a much better idea.
In my limited experience and insulated container (like the ones for the Nalgene) work for a couple of hours at around 32f.
(if you start with 750ml/1 L) for lower temps you need a vacuum flask ("Thermos")
A mate has used the REI flask down to -40 several times, it works well for several hours.