The thermostat controls fuel enrichment. If it is bad it will dump fuel like crazy on start up. Also, E46's have MAP thermostats, they are prone to failure and require replacement. Check the wiring connection to the thermostat it self, and check the temp sensor.
91 318is - M50NV (gone)
02 WRB Subaru WRX EJ207 forged, 320 AWHP stock turbo.
85 - 325
02 325i Sedan