Does MOSFET switching gate drive current depend on supply voltage?

I am using a 3-phase MOSFET driver to drive power MOSFETs for a motor controller. When I connect the circuit to a 24V supply (H-bridge supply) and enable the switching at 25 kHz, the driver gets warm. However, when I connect it to a 40V supply (for the final application) the MOSFET driver gets much warmer. Is the driving current supposed to increase with increased supply voltage? I am not sure because the gate-source voltage on the high-side MOSFETs is the same; the driver just needs to supply 40+Vgs to the gate instead of 24+Vgs to the gate. If the gate charge is the same, why would it take more current to drive it at a higher drain voltage?