I have a tankless water heater. After I finish to use hot water and I close the faucet, the water heater starts a fan and make a typical noise, it's very typical and expected. I guess it blows off excess moisture or similar.
I noticed however, that when I flush a toilet (only the one of the three toilets I have), the moment toilet valve stops the stream of cold water, my tankless heater starts the same noise as when you shut-off hot water. This leads me to believe that some hot water is pulled in when flushing a toilet. I closed the output hot water valve on the heater and - obviously - it does not make the noise when I flush that toilet. Also, the "in use" light of the water heater does NOT turn on when the toilet is being flushed, unlike when you open hot water "explicitly".
I also made another experiment and if I open the faucet of the tubs, fully on cold, when I shut it I also get the same reaction from the water heater.
I suspect I'm literally draining energy down the toilet every time I flush, and I'd like to understand what is going on.