Kaz's comments illuminate some of my confusion associated with the 1997-2005 service manual .pdf that I have been looking at. My preference is to work from paper service manuals; but, my 2000 service manual is locked up in the trunk of the NSX in secure storage for the winter, so .pdf it has to be. The 1997-2005 .pdf has missing pages and more importantly doesn't seem to have complete schematics which makes it hard to be definitive about your specific problem (but, somebody scanned and put the document together and posted it for free so I don't complain about free).
From the 1997-2005 service manual, the 1997-1999 models have the 'conventional' type of temperature gauge measurement system with external sender and based upon the test resistance measurements for the sensor in the 1991 SM, looks to be the same from 1991 - 1999. Because the schematic of the guts of the coolant temperature gauge are not available and I have never gutted one I can't be 100% certain; but, my guess is that this is a two coil gauge movement. The changing resistance of the external sensor (at temp goes up and down) alters the split of current between the two coils causing the needle to move. So the gauge is sensing the change in current flow through the external sensor. If I am correct that is a pretty common system.
The 2000+ is where it gets interesting. With Kaz's comments providing guidance, the few pages of the 1997-2005 SM which are available covering the gauge become more clear. The 2000+ coolant gauge no longer has the conventional sensor and the gauge 'sense' wire is connected to the ECU. This does create some uncertainty. The ECU could be outputting a voltage signal to the temperature gauge in which case the temperature gauge has switched from a current sensing gauge to one that just measures a voltage. The ECU could have the output to the gauge just be an (internal) open collector transistor which is operated in pulse width modulation mode to simulate the changing resistance of the old temperature sensor. In this case the temperature gauge would remain a current sensing gauge. I am betting that the gauge remains a current sensing gauge because switching to a voltage sensing gauge would require that the ECU be equipped with a digital to analog converter on that port. The PWM output just requires a simple digital port just like all the ports for injector control, coil control, fuel pump, EGR ..... D/A converters cost more money than a digital port and would be a bit of an oddity in an automotive environment where analog voltage control is definitely not the norm. My bet is that the coolant temperature gauge in the 2000+ remains a current sensing gauge. The test procedures for the 2000+ gauge sort of suggest a current sensing gauge; however, the manual has one test procedure where you disconnect the ECU A connector (contains the sense line for the gauge), turn the ignition on and then measure the voltage between A18 and ground. However, its not clear whether this is between A18 and ground on the ECU side of the connector or between A18 and ground on the harness side of the connector. The SM says to check for approximately 5 volts. If that is on the ECU side, this would screw me up because a digital PWM output normally has no voltage on it unless they are trying to fake an analog voltage output by using an internal pull up resistor. - in which case the gauge is a voltage sensing gauge. All very confusing.
I would bet (easy for me to do when its not my gauge that could potentially be toasted) that the 2000+ gauge remains a current sensing gauge. Visual examination of the gauge assembly to confirm that it is externally identical and retains the same number of connectors as the 1991-1999 gauge would support this. Beyond that, it is pretty much going to be up to testing to confirm. If there are clear terminal markings on the outside of the oil/temp gauge module, you might be able to arrange an external test of the gauge connected to the sensor to see if the needle gives you a 'correct' movement. This would save you the hassle of R&R of the gauge cluster only to find that the gauge is not compatible.
Watching with interest! You must really want the appearance of the 2002 gauge because this is a serious amount of effort to go through.