I would plug in my Kill-a-Watt multi-meter. (The Kill-a-watt is about a kilobuck worth of meters in a 20 dollar box) it measures frequency and voltage.
Someone posted about low voltage increasing current causing more heat in connections, Though he is correct,, He has no understanding of ELECTRONICS.
Your cell phone charger puts out perhaps 10 watts (5 volt, 2 amps) max. This is less than 0.10 amp at 120 volts,, So if the thing is not quite 100% efficient (And it is not) it might draw 0.11 amps on 120 volts, perhaps as much as 0.15 if voltage drops.. On an outlet desigend to pass 100 times that much current, This is NO LOAD and thus the added current will not cause heat.
HOWEVER a HIGH voltage will cause excess heat on devices INSIDE the power supply.
Either way.. Voltage may be the problem Press the V button on the Kill-a-watt and report the display.
NEXT is frequency. Many of those small electronic devices are kind of particular to frequency.. Press the Hz button on the Kill-a-watt and report the findings.
Some devices if the Hz is off.. can get very hot.
Finally we have the generator itself.. I will list 3 classes and examples. Pick one please (The one most like yours)
1: Class A built in like an ONAN or GENRAC usually 5,000 watts or more
2: Open frame traditional generaters where the motor runs at 3600 RPM, So many examples I can not begain to list 'em all.
3: Inverter generators such as teh Honda EU-N000i or Yahama EF-##00i units.
