Help us help you. By posting the year, make, model and engine near the beginning of your help request, followed by the symptoms (no start, high idle, misfire etc.) Along with any prevalent Diagnostic Trouble Codes, aka DTCs, other forum members will be able to help you get to a solution more quickly and easily!
We'd need to know more about the specific vehicle. Year/make/model/engine?
P0135 is for the B1S1 O2 heater circuit, I believe. I don't know the criteria off the top of my head, but I'd be surprised if the PCM commanded Open Loop for that fault alone. It's more likely the result of a misfire, IMO. Is there a noticeable misfire before Open Loop kicks in?