The K rating is basically defined as the type of light that is emitted by a perfect blackbody radiator that is at that temperature (in Kelvin).
Simply it defines the spectrum of the light... lower K rating is a warmer light with more yellows and reds emitted. The higher the k rating, the more blue or cooler the light is. This warm vs. cool has no actual relation to the temperature of the bulb (actually, nor does the K rating of the bulb).
Keep the wattage the same and look for lights that meet your needs. 10,000K oand actinic bulbs are OK for most SW tank applications, though 15k and 20k bulbs are available now. I'm not that into SW so you might ask if the critters you have need that kind light.