Hello, my name is Mark and I will try help you with this.
As it seems to be better after being allowed to warm up then that would suggest a possible fault with the engine temperature sensor.
A scan tool that can show live data is the best way to check it or you could do a resistance check of the sensor.
An air filter would not improve in condition as the engine got warmer.
Although at such a low mileage it probably hasn't been serviced every year as it should have been regardless of the mileage.