You will most likely find that the add-on box also connects to what may look like an electric fuel injector that is tapped into the control pressure line to the warm-up regulator. That would be the frequency valve that is acting to bleed off pressure & regulate the mixture when in closed-loop mode (when the O2 sensor is hot enough to output some voltage signal).

Not that I'm recommending removing anything, but let's just say that that it wasn't there when your car left the factory. In fact, if it was/is malfunctioning, it may have been the cause of your warm-up regulator 'problem' - I'd try resolving that before trying your new part; may save you some $$$.

__________________
Current rolling stock:
2001 E55 183,000+ Newest member of the fleet.
2002 E320 83,000 - The "cream-puff"!
1992 500E 217,000+
1995 E300D 412,000+
1998 E300D 155,000+
2001 E320 227,000+
2001 E320 Wagon, 177,000+

Prior MBZ’s:
1952 220 Cab A
1966 300SE
1971 280SE
1973 350SLC (euro)
1980 450SLC
1980 450SLC (#2)
1978 450SLC 5.0
1984 300D ~243,000 & fondly remembered
1993 500E - sorely missed.
1975 VW Scirocco w/ slightly de-tuned Super-Vee engine - Sold after 30+ years.