This is similar to shooting in the rain. Splashing water can ruin your equipment if it's not weather sealed.

The temperature of the water doesn't matter. As long as it's not boiling hot, it's equivalent whether it's cold or warm. What matters is whether the water gets inside your equipment.

I'd say there are four approaches to do this:

1. Use a telephoto lens and shoot from as far as you can, so far that water doesn't splash that far.
2. Arrange yourself a glass wall somehow and shoot from behind the wall. Then your only issue is humidity, but if you crank up the ventilation and do the recording quickly, you can minimize the humidity damage.
3. Use a cheap camera (+ cheap lens if it's an interchangeable lens camera) and treat destroyed equipment just as a loss; a fact of life. I'd say that if you don't purposefully splash on the equipment, the probability of damage will be small but not zero, so I can't promise you won't destroy your equipment.
4. Use a pro interchangeable lens camera + a pro lens. For example, Canon 6D and 5D series cameras are weather sealed as are R and RP (I'm not familiar with other brands but they probably too have sealed camera bodies). There may be differences in weather sealing quality, and typically more expensive cameras have better sealing. The lens requires weather sealing too, but L zooms have this sealing. Some lenses require a UV filter to complete the weather sealing (example: Canon 17-40L).

Note that approaches 2-4 may lead to water splashing on glass (either the glass wall or the lens glass), affecting the optical quality of the image.

I'd probably prefer (1) but it requires a large room. The benefit of (1) is that water doesn't affect the optical quality of the image. Note, however, that shooting from near with a wide angle lens and shooting from far with a telephoto have different amounts of background compression.

You can also try setting up a rain cover on the camera, but it's not perfect as it has to have a hole for the lens front element.