Ian, I have been already doing exactly this type of simulation in GT DRIVE since 2007 (NEDC, not FTP-75, but shouldn't matter), so I feel I have some (minor) authority on the subject. I am also writing a thesis on this subject.
First of all, modern gasoline engines do not use cold-start fuel enrichening to quite the same extent as they used to for obvious emissions reasons. The key word is catalyst heating, and most engines use a combination of measures, predominately retarded ignition timing, to raise the exhaust gas temperature and thereby get the catalyst to light-off as quickly as possible.
Nonetheless, in my models I use a very simple fuel quantity multiplier by some factor (in the order of 110% -- don't misunderstand, that means 10% in addition) during the period of catalyst heating, which in the cars I have investigated are under a minute. One of my mentors' favourite sayings is, "Make a simulation model as simple as it can be, and complicated as it needs to be."
Increased friction during warm-up is done internally in GT DRIVE if I supply a coolant or engine-oil heating curve over the course of the driving cycle simulation. At least in the NEDC cycle, many cars reach 60°C oil temperature between 350-450 seconds, and 90°C (full operating temperature) by 800 seconds, corresponding with the end of the ECE urban phase and start of the EUDC extra-urban phase.
During the initial phase of warm-up, the engine operates at an increased idle that is a function of coolant temperature. Again, given this function and a coolant heating curve (typically reaching 60 and 90°C somewhat sooner than the engine oil), then I know precisely what the mapped idle speeds.
Diesel engines do not use fuel enrichment at during cold-start at all, but also features retarded injection timing, increased idle speed (again a function of coolant temperature, and there may be auxiliary coolant glow-plugs in use), and different EGR settings than a warm engine. In my simulations I never use a cold-start multiplier. The internal friction compensation as a function of oil temperature suffices.
With proper model build-up and calibration, I have found excellent correlation with road-test data.