Consider having a circuit which consists of a battery and one resistor.
$V = 10$ volts, $R = 5$ ohms, so $I = 2$ Amperes, and $P = 20$ watts.
If we double the voltage and resistance, the current will be the same and the power will be equal to 40 watts, hence the resistor will be hotter than the first case.
Now here is the silly question.
The current in each of the two cases is constant and equals the current of the other. The speed which charges move across the wire is constant. So why is more heat generated while the speed of charges is constant? I know that the potential is doubled, but the potential is potential, and we can't make use of potential energy unless it is converted to kinetic energy. How can the resistor make use of this (potential) energy, the mechanism which the resistor turns potential energy into heat.