You can sync the white balance setting across multiple photos, which will cause each to have exactly the same white balance setting for temperature and tint.
In your case, it sounds like the scene's color temperature is different from one shot to the next. In that case, you'd need to manually white balance each image. For time lapse images, if the color temperature of the scene's lighting is changing over time, it is a real challenge to post-process a lot of images to yield the appearance of constant color temperature throughout the sequence.
Oh dear...I'm in a bit of trouble then! Thanks for your clarification!!
Lots of good info from Mike.
That said, if you have the same object in every photo that is supposed to be white or a shade of neutral gray, you can use the eye-dropper on that object to set the white balance individually for each photo.
One of the catches here is that if the light is changing in the sequence of photos based on the time of day, then the photos will not look natural if you set them all to the same white balance.
How I do this is to have the white balance constant throughout the series and then when I assemble the time-lapse from an image sequence in Photoshop (best way to generate the timelapses). Then I do a faded adjustment layer that corrects the white balance over time. If you don't want to go Photoshop for this, Jeffrey Friedl created a very useful plugin that allows you to fade develop settings between two extremes for a series of images: Jeffrey Friedl's Blog » Jeffrey’s “Timelapse Support” Lightroom Plugin. This allows you to have two extreme white balance settings at the two ends of your time-lapse and fade in between. It can also do pan and zoom although that is much easier done when you assemble the time-lapse in Photoshop.