Thermostat needs a swap. Think how many cycles they do.
Now on the O2 Keep in mind its possible may not throw a code but yet be defective.
The O2 sensor reads unburned oxygen in the exhaust, and generates a voltage signal that is proportional to the amount of oxygen in the exhaust. The signal can vary from a low of about 0.1 volts up to a high of about 0.9 volts.
A low voltage signal indicates a lean fuel mixture. A high voltage signal indicates a rich fuel mixture. The engine computer uses the O2 sensor's
input to balance the fuel mixture during closed loop operation. A bad sensor may prevent the system from going into closed loop, and usually causes the fuel mixture to run rich causing an increase in fuel consumption and emissions.
You asked about fuel trim on the downstream but its only a tattler for the converter. * Note* A downstream oxygen sensor built in or behind the catalytic converter works exactly the same as an upstream O2 sensor in the exhaust manifold. The sensor produces a voltage that changes when the amount of unburned oxygen in the exhaust changes. However it only monitors the efficiency of the Cat itself.
The PCM monitors converter efficiency by comparing the upstream and downstream oxygen sensor signals. If the converter is doing its job and is reducing the pollutants in the exhaust, the downstream oxygen sensor should show little activity (few lean-to-rich transitions)).
The Downstream sensor's voltage reading should also be fairly steady (not changing up or down), and average 0.45 volts or higher.