bro...almost same situation....cold engine....full scale deflection of the temp gauge.and my fuel gauge was also showing empty all of the time regardless of actual qty.in my case the fuel level sender unit was faulty,shorting to the power supply wire and therefore frying the instrument cluster.....had to fix the fuel level sender first and then replace the instrument cluster....hope yr issue is simpler.....
Hi bro goggle for e46 meter self test or hiden function menu...
Im also a newbie here....
May be your gauge or the fuel sender/float is malfuntion....just my 2cents. ..