This code refers to the front oxygen sensor on Bank 1. The heated circuit in the oxygen sensor decreases time needed to enter closed loop. As the O2 heater reaches operating temperature, the oxygen sensor responds by switching according to oxygen content of the exhaust surrounding it. The ECM tracks how long it takes for the oxygen sensor to begin switching. If the ECM determines (based on coolant temp) that too much time elapsed before the oxygen sensor began operating properly, it will set P0135.
A lot of problems come with corrosion of the contacts. I would unplug the connector, look at the contacts, and replug it 4-5 times and then see what happens. It should reset if all is working correctly in a few restart/run cycles.
The O2 sensor that we are talking about is the one on the exhust manifold.