While a round trip can take nearly a minute, your foot is at one extreme. It's only path available is back towards your core so it does happen within a couple of seconds.

The effect happens similar to a coolant line with a radiator. Your foot expels a lot of heat quickly because of the temperature difference, cooling the blood off. That now cool blood travels back up to your core, immediately absorbing heat from your much warmer core area. So what happens to your foot, the reverse happens in your core with the same blood.

The greater the difference in temp at your foot, the faster it expels heat, the cooler the blood, the faster it absorbs heat from your core once it gets back up there.

So you don't need to wait for the blood in your core to reach your foot to feel cooler. You just need cooler blood to enter your core.