my 2009 5-speed manual Toyota Corolla has been having a bit of an odd issue lately. When first starting the car when it’s been a little colder (1-5 degrees Celsius), it has been grinding third gear for the first 2-4 shifts despite the clutch being fully depressed. It seems to go away when the engine is warmed up is this normal?or is there reason for concern
Given the age of the vehicle and if the transmission has never been rebuilt, it's likely that the synchromesh gears are worn. These are the components of the transmission that help you do a smooth shift even if you haven't quite hit exactly the right target RPMs. This is a natural consequence of age and is part of having an older car: slow shifts are smooth shifts.
This issue is magnified when the temperature drops as the gear oil is also cold and doesn't really feel like lubricating all the components that are needed for smooth shifts. Once that oil warms up, you'll have less trouble shifting without grinding.
In short, your car is asking for slower shifts when it's cold out. When my car was really cold, I would shift out of lower gear, pause with stick out of gear for a beat and then try to shift into the higher gear. The car seemed to appreciate that I was giving everything a little longer to work as its old bones creaked on our way to work!