One problem related to radiator has been reported for the 2001 BMW 740. The most recently reported issues are listed below.
In March 2007 low coolant warning caused me open hood and add coolant three times before I took car to BMW dealer ,who diagnosed cracked plastic reservoir in radiator and separate coolant tank. Each time engine had overheated due to a lot of pressure under radiator coolant cap. Needed much time waiting before opening to add coolant. This was defective materials and not normal wear and tear breakdown. Every preventive maintenance has been done by book on this BMW. Manufacturer disclaimed responsibility as car out of warranty by few months. Car had 54,000 miles. Plastic was found hardened by heat and brittleness cracked the same. 339 other BMW 740il owners have filed petition on internet for same cracked plastic radiators (on BMW 740i ,and IL models between years 1995 through 2001. BMW ignored our pleas for free replacement. Major safety issue not expected on premium car like this.