Its probably a problem with the Carbs. Series 3's have Zenith Stromburgs, that are notorious for problems. Most likley the problem is in your choke. Check to see if your choke is functioning properly. These carberators realy hate to start without the choke on initial startup.
Worse case scenario is you may need a new choke cable. Because the fact that the car runs fine when hot suggest that choke is screwy and may need attending.
Hope that helps.