If you are under 6000K lighting and you set the camera to 10000K white balance, the color temperature you end up with hasn't changed, it's still 6000K lighting with a 10000K color temperature setting, what changes is the color.
I think you're asking how much warmer than neutral will it look, but to do that, you have to have a frame of reference in terms of how you label degrees of warmth. Obviously there's a 4000K difference between 6000K and 10000K, but does that mean anything to you (or me)?
The other problem is that changes in Kelvin are not linear in terms of how much they affect the warmth or coldness of the color, which is why the MIRED system was developed. In other words, if you want to shift a 3200K light to 3600K -- by 4000K -- it's not the same strength of blue gel as it would if you wanted to shift a 5600K light to 6000K, even though that's also by 4000K.
So in terms of the change in warmth, most people use as a frame of reference a CTO (orange) gel or a CTB (blue) gel, or they use camera correction filters, but again, you'd need to know just what they look like if I told you, for example, that the 4000K shift would look like you added an 81EF filter to the camera in terms of extra warmth (I don't know if that's the correct filter by the way, I'd have to use the MIRED system to determine that).
Once you calculate the MIRED shift between 6000K and 10000K, for example, you could get a swatch book of Lee or Rosco gels and find the gel that does that amount of color correction.
Basically how much an orange light shifts yellower or redder is more of a shift along the GREEN-MAGENTA axis, not the color temperature. So if you set the camera to 10000K and you thought it looked a little too yellow, some cameras would allow you to also make an adjustment towards or aways from green, so shifting a little towards the magenta would take some of the yellowness out. It's not exact but it works well enough until you get into a final color-correction. Obviously you can use gels to make orange more reddish or yellowish. For example, CTS is more yellow than CTO if you were using those gels (there isn't a similar yellower version of CTB gel though.)
Truth is that for digital cameras where you can adjust the color temperature, most people just try different settings out and look at a monitor, that's how they know what 10000K looks like under 6000K lighting.
In terms of limits, you'd have to test and look at them carefully in post to see if you are running into artifacts by pushing the color temp setting too far from normal. Generally sensors have a natural preference for daylight balance, somewhere in the 5000K range, and to make them correct under 3200K lighting, they have to boost the blue channel to compensate for the weaker amounts of blue wavelengths under tungsten lighting, and thus the blue channel is noisier than when the camera is set to daylight. This is one reason why there is no reason to use 85 correction filters with the camera set to 3200K in a digital camera today when shooting outside in daylight, you're better off setting the camera to daylight. So in terms of the far end, setting the camera to, let's say 11000K, which I think is the highest the Alexa can be set to, you're probably OK in terms of noise but if you are baking in that color by recording ProRes instead of Arriraw, then your image being so warm now has less blue information in it and if you try to color-correct this back to neutral, you may find that blue colors are a little faded looking or hard to separate from the warm colors.
Now the other way, shooting in 3200K lighting but setting the camera to its lowest color temp setting, 2000K, to get a blue cast, you might find the blue channel to be getting a bit noisy depending on your ISO rating.