how can i encourage them to breed?
There are hundreds of resources on the Internet to help you learn to spawn Corys. Google "Spawning Corys."
i've heard that doing a cooler water change can get them to spawn, does that work?
It can, but there are no guarantees that it will. If it where that simple, who would not be successfully spawning Corys?
and when i do that, do i add cold water and also turn the heater down a bit, or leave the heater as it is?
Different people have different thoughts on how to spawn Corys. Personally, I do nothing but feed them the best food that I can and I do 50% water changes, 2X per week. I do not personally employ and premeditated spawning triggers and I have spawned 61 species, so I just do what works for me. I don't even use spawning mops, so I would not recommend that you follow my lead. lol.
Do your research and determine what makes sense, for you. There are
no absolutes. - Frank
P.S. Anyone who tries to claim, "This is how it's done" - doesn't understand the intricacies of spawning fish. At best a person should state, "This is what worked for me." That does
not mean that it will work for you.