Render is a word with many meanings; in terms of food product, it does specifically involve heating. You're wrong on that point Choco, but I feel like debating semantics on this is pretty ridiculous. These long winded totally pointless arguments y'all get into probably turn away a lot of newbies.
12. To reduce, convert, or melt down (fat) by heating.
Putting butter in coffee is, quite seriously, no different than putting cream in coffee. It's essentially the difference between ice and water.