It doesn't make a huge difference. If you start with cold water you may damage the pot if you place it directly on a hot burner. Warm water will take less time to increase to a boiling temperature, and may prolong the life of your pot.
It's best to start with cold water if you are boiling water for tea. I've done both, hot and cold water, before to make tea and it tastes the same to me. When boiling water to cook foods, it doesn't really matter.