You'd need to go into the menu of your body and find out what Picture Control is set. Neutral should definitely yield less, but if you are shooting jpeg, the images might look too bland. The other option is to use whatever Picture Control is set - but you can go in and have the option to lower the saturation in-camera through that Picture Control setting. You can also tweak your contrast as well as other settings if you choose.
If that doesn't work well enough, then change to a different Picture Control (stay away from Vivid as that's too colorful and contrasty). Tweak any individual settings if necessary. If that doesn't work, then try yet another Picture Control. Off hand I can't remember all of them. I'm pretty sure mine is set to Standard which might be the default. All you can do is to experiment.
And if shooting jpegs, any white balance above 5500 is getting into the warm colors. At times even 5500 is too warm. You have to consider the environment you are in. If you are indoors with tungsten lighting (the old fashioned light bulbs that give off a brownish coloring), then you'd have to choose tungsten as your white balance to color correct the image in camera. If you are shooting RAW or using Photoshop or Lightoom, then you can easily change your white balance during post processing. Otherwise, try the suggestion about tweaking the Picture Control in camera.