Coolant temp is one of the sensors the ECM uses to control the EFI system.
Without a t-stat to regulate coolant temp properly, the sensor may not have proper temp info to supply to the ECM. Another possibility is having no t-stat may not provide the correct coolant flow to the temp sensor, and again a bad reading to the ECM.
O2 sensor is in the exhaust system, and without correct data from it to the ECM, the EFI system will stay in the open loop condition.