An adapter is just simple wires to let a US plug connect to a foreign outlet, however the voltage stays the same (240v). A converter lowers the voltage to 120.
some math:
A hotlogic mini uses 40W at 120V
so how many amps is it drawing
W=V*A so A=W/V 40/120=0.3333A
what is the resistance
R=V/A 120/0.3333=360 Ohms
so a hot logic has a resistance of 360 Ohms
Now lets see what happens if I give it 240 volts.
Watts = Volts*Amps
V=240
how many amps will it draw A=V/R
we know R is 360 so 240/360= .6667
.6667A*240V=160W
So if you use an adapter instead of a converter it is putting out 4x more heat then it is rated for.
It is possible that it has a thermostat to prevent overheating but it does not seem like a good idea to rely on it