It could also be related to the Mpemba effect - hot water freezing quicker than cold (for which I think there are still competing explanations)
It's definitely not related to the Mpemba effect. The cooling effect of tea is allegedly a biological response to the imbibing of a hot drink in a hot climate. The Mpemba effect is a yet to be a universally accepted physical phenomenon explained by a universally accepted set of physical processes.
I was familiar with the Mpemba effect before Mpemba discovered it but only just. He observed the effect in 1963 and I received my warning in 1962.
My grandmother wouldn't let me put out warm water for the birds in winter telling me that it would freeze faster than cold water and deprive the birds of a drink sooner than giving them cold water would. I accepted her assertion without further thought or challenge, after all, grannies are never wrong are they? Time and lots of experiments performed by others suggests that her assertions were correct.
I never thought about the Mpemba effect again until I was doing a PGCE in 1983 and was idly leafing through some Association of Science Education magazines in Leeds University's Centre for Science Education. I'm still not curious enough to perform any experiments to investigate the effect. They'd be as exciting as watching paint dry and even less exciting than the series of experiments that I performed as a combustion engineering undergraduate to determine the minimum air flow required to maintain combustion in metallurgical grade coke that had been doped with a range of copper salts.
I wonder how and/or where my granny acquired the knowledge.