A friend of mine claims that children should never have the heater on during the night because it helps viruses and bacteria to grow.
An other person claims the opposite and the child should never feel cold.
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Bacterial growth isn't going to be sufficiently slowed at temperatures that humans are comfortable with. One of the reasons the bacteria that infect us are still around causing us problems today is because they like a lot of the same conditions we do! Many infectious bacteria are mesophilic, meaning they like temperatures between 20C and 40C - the human body is normally at 37C.1
A problem with cold temperatures is that the child may have a harder time breathing due to bronchospasm - a condition where the airways become narrower - and cold dry air causing irritation.2 Colder air can also cause the shell on the influenza virus to harden, making it more infectious3.
Another consideration that you didn't mention is relative humidity. Both heaters and air conditioners can change our body's ability to dissipate moisture. When the moisture evaporates too fast, we can have irritation to our skin, nose, and throat.4
It's probably best to keep the temperature and humidity at a level where the child is comfortable sleeping, within reason.