Hi @imnuts ,
Is the engine actually overheating or is the temperature gauge just showing that it is getting too hot i.e. faulty temp sensor perhaps?
Here’s the 2001-2005 Kia Rio Service Repair Manual + Wiring Diagrams.
In the Engine Cooling > Electric Cooling Fans section it shows how to test the fan and the temperature sensor.
Also wondering if there may be a problem with the water pump, (impeller blades worn, broken?) When normal driving the airflow through the radiator may help in cooling the coolant but when idling or low speed there is no or little airflow through the radiator so the fan turns on but maybe if the coolant isn’t being pumped through quick enough the coolant is hotter and the temp guage goes up. Just a thought.
In the Engines 1.5L 4- Cylinder section on p.22 of 59 ( no actual page numbering in the manual so have to use the pdf page number) it shows how to remove the water pump so that it can be checked etc.