Does Hot stuff get Colder than Warm stuff when cooling?

I know, that it is a scientific fact that hot water will freeze much faster than lukewarm water when exposed to temperatures below freezing point. Briefly this has to do with the movement of the molecules. I wonder however, if I for example make a cup of tea, and leave it to cool off; will it become colder than the surrounding temperature? This is an observation I’ve made. “Cold coffee tend to be colder than liquids which haven’t been heated previously.” – or is it just a “contrast thing”..?