It's red and blue light that activates growth the most. The reason bulbs with a warm colour temperature are chosen is because there's more red end of the spectrum, which is the most important. Think weed growing...
You can get LED lamps on eBay which are red, or red and blue, they'll be most efficient as they're only outputting the wavelengths that stimulate growth, and they're LEDs which are efficient anyway.
Just search eBay for LED grow lamps and choose one that suits you, they'll all be far better than a warm white lamp. They're all for growing "herbs"