need to scan it live data see what its doing no point guessing or throwing parts at it.. if doing it when at running temps would suspect a 02 sensor or temp sensors maybe ,,
how the system works where engine cold the coolant temp sensor shows temps the ecu knows to use a preset choke cold start map until engine reaches a set temp around 60c it begins, ie the engine under this temp runs faster,,, the 02 sensors are a closed circuit type and dont do nothing until 600c ie ie a 02 sensors for signal makes its own voltage from hpow its made ie around 1.6volts and 0.45volts normal for correct fueling when exhaust is hotter than 600c, now wide band 02 sensors as mini have also have a heater circuit this is used for when the 600c is not reached so ecu can monitor the voltage and fuel car,, ie car when at full running temps switches to closed loop running,
this all said what can effect this working wrongly , 1 is the cat is blocked with oil burn crud this is common and reduces the hot gases reaching the down stream 02 sensor this can cause fueling issues as down stream 02 runs slower than up stream and is more important for fuel trim over time,, the up stream runs faster and controls mixture trim faster than down stream,
another issue might be cat has a hole in it on live data can tell if both sensors read the same voltages,,
or when blocked the 02 sensors will show one at top of volts and other at bottom.. live of a 02 sensor makers say 60 to 120k less on oil burning cars or cars with coolant leaks etc,
also the fueling system has a another tempo sensor that measures outside temps as ref point and also has a inlet maff temp sensor as well for temps in the inlet manifold,
as you can tell not the easy thing to work out even someone who works on them all the time will have a merry dance with it, also would only use someone who really knows the facts and dont use the try this approach