I'd don't think it's fat burning but it would be called keto coffee:

butter
coconut oil
salt
artificial sweetener if you must (almost guarantees it will be too good delicious and you'll over consume - thus fat ADDing rather than BURNing)

whipped up with hand blender. I think the little bit of protein or somthing in the butter grabs onto the coconut oil and helps with better emulsification.

Don't drink it to lose weight, it's suggested to EAT your calories by some. I'm with s93 these days - black, no sweetener and watered down. Just something hot.

It's not a bad thing tho, kind of like a morning fat bomb, but you're body has already prepped you for that ramping up morning glucose production and cortisol to get up and get going, i think