Yes, usually it is a coldwater change, but also some other conditions have to be met in the tank. Nitrate, pH, hardness of the water, should all be within reasonable ranges. In short: if the cories feel comfortable and happy, then a coldwater change might very well trigger them to spawn.
My Brochis Splendens (Emerald catfish) decided to spawn when we had a major storm with lots of rainfall over here; I didn't do a waterchange at all. I've read somewhere that some people believe that the catfish can actually detect a drop in atmospheric pressure, which might trigger a spawning.