Will heaters burn plants?

So long as the plant is not actually rubbing up against the heater I doubt you will see any problems. I have had a few plants growing near my heater in the past and it never seemed to make a difference, though I had a lot of water flow in the area. I currently have my heater living behind a curved piece of driftwood so that it is not visible except from the side, which looks nice since I have ferns and moss growing all over the wood. Some Java Fern and Bolbitis wound up weaving around and growing near the heater with no problems.

with a submersible heater, you can lay it along the substrate in the back. This is best with heaters that have an external temp. adjustment.
Pulling the heater out to make a temp adjustment is a pain in the butt when you have it laying accross the bottom of the tank in the back behind all the plants and decorations...