The thickness is likely the bacteria, it's the slimy clear part. The yeast is the brown stringy part. Higher temperatures and sugar content are going to influence the consistency as well as your total volume of fluid. As others have noted, your scoby might be too big for the container and volume of tea. I use a 1 gallon jar and my scoby is about 3 inches thick. My brew cycle takes 7-10 days and I take out a little over half the volume of raw kombucha each time.
Just a note, higher temperatures will really speed up the brew, so keep that in mind and taste more often.