Try removing the MSI AB profiles, restart your system, and see how it goes. But if your GPU has the fan stop feature, the fans again won't kick in unless manually started via any app.
You still haven't mentioned the
exact model number of your GPU though. Gigabyte is the brand.
As per this databse there are 6 models in total, and I'm almost certain all these cards have Gigabyte's "3D Active Fan" semi-passive cooling tech, where fans will remain off when the GPU is in a low load or low power game.
https://www.techpowerup.com/gpu-specs/geforce-rtx-3070-ti.c3675
GIGABYTE AORUS RTX 3070 Ti MASTER
| 1575 MHz | 1875 MHz | 1188 MHz | 324 mm/12.8 inches, Quad-slot, 3x HDMI 3x DisplayPort |
GIGABYTE RTX 3070 Ti EAGLE
| 1575 MHz | 1770 MHz | 1188 MHz | 283 mm/11.1 inches, 2x HDMI 2x DisplayPort |
GIGABYTE RTX 3070 Ti EAGLE OC
| 1575 MHz | 1800 MHz | 1188 MHz | 283 mm/11.1 inches, 2x HDMI 2x DisplayPort |
GIGABYTE RTX 3070 Ti GAMING
| 1575 MHz | 1770 MHz | 1188 MHz | 320 mm/12.6 inches, Triple-slot, 2x HDMI 2x DisplayPort |
GIGABYTE RTX 3070 Ti GAMING OC
| 1575 MHz | 1830 MHz | 1188 MHz | 320 mm/12.6 inches, Triple-slot, 2x HDMI 2x DisplayPort |
GIGABYTE RTX 3070 Ti VISION OC
| 1575 MHz | 1830 MHz | 1188 MHz | 320 mm/12.6 inches, Triple-slot, 2x HDMI 2x DisplayPort |