The back of the FCTM (Section 8?) contains the management guide and provides such recommendations. Also the QRH non-normal section of the checklist instructions should provide some ammo too.
I was looking at that section for some guidance, too:
Engine Failure versus Engine Fire After Takeoff
Engine Failure versus Engine Fire After Takeoff
The NNC for an engine failure is normally accomplished after the flaps have been
retracted and conditions permit.
In case of an engine fire, when the airplane is under control, the gear has been
retracted, and a safe altitude has been attained (minimum 400 feet AGL)
accomplish the NNC memory items. Due to asymmetric thrust considerations,
Boeing recommends that the PF retard the affected thrust lever after the PM
confirms that the PF has identified the correct engine. Reference items should be
accomplished on a non-interfering basis with other normal duties after the flaps
have been retracted and conditions permit.
No distinction between thrust or no thrust with an engine fire that I can ascertain.