Is it an illusion if reheated tea burns my tongue but tastes cold?

I like drinking hot tea or hot water, but I don’t like burning my tongue. I believe that certain processes/procedures to prepare the hot tea (or hot water) are more likely to achieve the desired results than others. For example, I could

• pour boiling water over tea leaves into a tea pot, wait 5 minutes, fill a small tea cup, and wait some more until the tea is cold enough (that I no longer burn my tongue). Or I could
• use a cooktop (hot plate) to reheat cold tea until it boils, fill a small tea cup, and then wait until the tea is cold enough.

My physical intuition has trouble to explain why the results of the different procedures should be different. I sometimes wondered whether I just developped some harmless superstition that creates the illusion that I am more likely to burn my tongue at the reheated tea, or that it would taste cold, or both at the same time (really).

Some days ago, I did a simple experiment, put some milk into the tea, and observed the mixing. The reheated tea had "convection bubbles", and a think (4 mm) non-mixing layer at the top. The fresh tea also had a non-mixing layer at the top, but it was thinner (1.5 mm), and the mixing was faster with no "convection bubbles". (However, the experiment was not "well controlled", it was not the same cup, not the same tea, not the same temperature, and it probably won’t be reproducible.)

The experiment gave me some idea what might be going on: There is some oil-like substance in the tea which is better "mixed" with the water for the fresh tea, and that substance tends to form a layer at the top that reduces the evaporation of the water. The evaporation probably cools the top surface a bit, and makes it less likely that I burn my tongue. However, even this explanation does not fully convince me: why should there be a difference in how well the oil-like substance is "mixed"?