No the tank doesn't have to be cycled. I would use filtration, as without movement the water will get stagnant......as for heat, I am sure most plants would grow better in normal tropical tank temperatures, which would require a heater.....But they wouldn't die without it, just not grow as well....
The main part is the lighting, research the plants you want then buy the light intensity that will keep them healthy. I would research all this on
www.plantgeek.net Why would you not want fish?

One or two lovely ones dress up a planted tank, and help feed the plants!