Really a good question, but I had a different view on this.
1. Nalacharitharam, which says by not washing feet after meals had lead to many problems , but this shows the worst effect, which pushes fear in us.
2. now, a bit of science... To control body temperature... Let's see how?
How Eating Affects Body Temperature
Eating generally leads to a slight increase in body temperature, as your metabolic rate increases in order to allow the digestion of food. Your temperature may increase by as many as 2 degrees F as the chemical reactions of the digestive process take place within your body. These chemical reactions are what produces the heat that causes a slight augmentation in body temperature.
And at the same time when you wash your feet with cold water (only) then the pulse points in your ankle where the blood streams gets closer to your skin gets cooler and moderates your body temperature.
This is my learning and assumption / prediction for a scientific background.
As I believe Every culture has a reason behind it, and is the same with ours too.
So before rejecting the words of elders try to understand the reason behind, even if they themselves do not know.
Thanks.