Content size fitter smooth growth with text

Hi,

I have a Text ui element that holds log and the text being added from time to time.
The anchor of the Text ui is at bottom, so new lines are added at the bottom.
Now the size just jumps to the longer size to take the new line into account, but I don't want it to jump, I want it to smoothly transition to the new height.
Does 'Content Size Fitter' support this? Do I have to take another approach?

Thanks!