I've been doing mine in an unheated basement. It stays cool down there. I think that a warmer temp would cause the culture to grow faster. Mine has been set up for a week and every day it is getting a darker green color. When I started it was a light blue from the fertilizer. I used tap water to promote the growth of algae that the phytoplankton eat.
Be sure to give it a nice swirl everyday. the phytoplankton will begin to settle on the bottom of the bottle, as the phytoplankton get more dense you will notice less settling on the bottom. After the first night I thought it crashed because all the phytoplankton settled on the bottom of the bottle and my water was just a light color blue. I gave it a gentle shake and it all mixed up again. I'll post a pic when my first batch is done.