Depending on the tones, turquoise and burnt orange can go well together. The more blue is in the turquoise, the more you want the orange to tend toward yellow. If the turquoise is more to the green side, you'll want the orange to tend toward the red, or even leave the orange spectrum entirely and veer towards magenta/purple. "Turquoise" can mean a lot of different things.
Personally, I think coral is a safer choice for more shades of blue-green. I do love orange but it can be a little tricky to work with.