The Physics Equation

Thermodynamics

A basic equation we can use to understand how a thermos does still allow heat flow is to look at the heat flow equation:

The purpose of a thermos is to hold in warmth or cold without help, so we can assume no heat transfer into the thermos. The sources of heat flow out come from the thermos lid and container.

Next, if we use the best thermos materials, the heat flow out from the container sides is zero because no heat flow can go through a reflective vacuum.

This shows that if you are using a perfectly vacuum insulated thermos, then the only heat flow is through the lid. The signs of heat flow, negative or positive, depends on if the thermos is holding a warm or cool substance.