Disable gpu / reduce power consumption on linux

I have a laptop with i7-10750H processor and RTX 2060 GPU. When using linux , I do not have any use for the GPU, so I would ideally like it to see it disabled or in a low power state to prolong battery life. I’m on Arch Linux on kernel 5.15.7 with this configuration (adopted from the official docs).

# I do not have the proprietary driver installed. 
❯ cat /etc/modprobe.d/nvidia.conf
blacklist nouveau
blacklist i2c_nvidia_gpu

❯ cat /etc/udev/rules.d/80-nvidia-pm.rules
SUBSYSTEM=="pci", ATTR{vendor}=="0x10de", ATTR{class}=="0x030000", TEST=="power/control", ATTR{power/control}="auto"
SUBSYSTEM=="pci", ATTR{vendor}=="0x10de", ATTR{class}=="0x030200", TEST=="power/control", ATTR{power/control}="auto"

which works fairly well. The idle power consumption is about 8-12W when on battery which I think points to the GPU being in low power state. However, when I connect the power supply, the laptop’s temperature goes up (CPU thermals from 45C to around 60C) and gets very uncomfortable to use unless put down on a desk. The fired udev events suggest that something about the GPU changes:

When the power supply gets plugged in:

UDEV  [1130.982555] change   /devices/LNXSYSTM:00/LNXSYBUS:00/PNP0A08:00/device:20/PNP0C09:01/PNP0C0A:03/power_supply/BAT0 (power_supply)
UDEV  [1131.086903] change   /devices/LNXSYSTM:00/LNXSYBUS:00/PNP0A08:00/device:20/PNP0C09:01/PNP0C0A:03/power_supply/BAT0 (power_supply)
UDEV  [1133.956517] remove   /devices/pci0000:00/0000:00:1d.6/0000:3c:00.0/wakeup/wakeup59 (wakeup)
UDEV  [1134.261055] change   /devices/LNXSYSTM:00/LNXSYBUS:00/PNP0A08:00/device:20/PNP0C09:01/ACPI0003:00/power_supply/AC0 (power_supply)
UDEV  [1134.321549] change   /devices/LNXSYSTM:00/LNXSYBUS:00/PNP0A08:00/device:20/PNP0C09:01/ACPI0003:00/power_supply/AC0 (power_supply)

When the power supply is unplugged:

UDEV  [1294.329131] change   /devices/LNXSYSTM:00/LNXSYBUS:00/PNP0A08:00/device:20/PNP0C09:01/PNP0C0A:03/power_supply/BAT0 (power_supply)
UDEV  [1294.514345] change   /devices/LNXSYSTM:00/LNXSYBUS:00/PNP0A08:00/device:20/PNP0C09:01/ACPI0003:00/power_supply/AC0 (power_supply)
UDEV  [1294.560940] change   /devices/LNXSYSTM:00/LNXSYBUS:00/PNP0A08:00/device:20/PNP0C09:01/PNP0C0A:03/power_supply/BAT0 (power_supply)
UDEV  [1294.717770] change   /devices/LNXSYSTM:00/LNXSYBUS:00/PNP0A08:00/device:20/PNP0C09:01/ACPI0003:00/power_supply/AC0 (power_supply)
UDEV  [1304.427565] add      /devices/pci0000:00/0000:00:1d.6/0000:3c:00.0/wakeup/wakeup59 (wakeup)

Is the GPU exiting out of the low-power state? Is that why the laptop gets hot? Is there a simpler way to disable the GPU completely when on linux? The laptop does not even get warm when connected to power supply on windows.