Is It Possible For An O2 Sensor To Work Well When Cold But Then Malfunction When Hot?

Does this O2 sensor look toast, like seriously burned out?

Unless an oxygen or air/fuel ratio sensor is physically broken the only way to tell if it’s good or not is to test it installed on a running engine. The way it looks is irrelevant.

Unlike Mike in NH, I haqve had several oxygen sensors trip the check engine light between 70 and 100,000 miles. I have done a lot of short trip driving.

When I have had hesitation when trying to accelerate , it was usually a dirty throttle body.