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You read those first. It is likely that elimination of one code will solve the other, so it is best to replace both relays on the firewall, and then the sensor itself. A new sensor should always be put in with new relays, however.
I agree...the Relays are cheap and often cure the problem. If they don't do it, you might also check the Coolant Temperature Sensor. Mine once had a bad connector there, which made the idle bad, which set off the code 34.