I have a Sony AC 100~240V 0.75-0.4A input and DC 12V 3A output adapter. I connected it to a peltier module that was drawing around 2.9A on both 110V & 220V. Initially I had connected the adapter to a 110V outlet, but there was a small hum from the adapter and it was hot really quick but when I tried plugging the adapter to a 220V outlet there was no hum from the adapter and also the adapter got only warm. So, does the adapter draw more current in a 110V supply? I don't have an AC clamp ammeter with me to measure the current, so there is no way to determine the current draw.
Yes, a universal input adapter will keep its output voltage constant when powered from (e.g.) 100-240 VAC. That means it's supplying the same output power.
Since input power is output power + losses, and power is voltage * current, the higher the input voltage the lower the input current. This is called a constant power load and is typical of switching power supplies.
XFMR Power ratings are defined for some safe temperature rise (Room + 40'C for example , depending on safety code) and full VA output only for linear loads. (~70% for bridge cap loads.)
Using 2.9 out of 3.0A rating I would therefore expect a ~60'C transformer when used at 120Vac and perhaps ~70'C if used in Japan at 100Vac. But then a Japanese Engineer might reason that 97% of rated transformer power is not a good choice. Always derate power of devices for expected long life.
Since conduction losses are both primary and secondary windings , worst case heat rise occurs from lowest primary voltage for primary current. e.g. 100Vac But output power and secondary losses will be the same.