You don't actually need to remove the air filter. What works very well, is to hold a piece of plastic or rubber hose, doesn't have to be that big in diameter, close to the air filter inlet, and hold the other side to your ear. You will be able to hear air noise very well as the car warms up from a cold start and, if the thermostat/WRD is doing its job, you will hear it shutting off slowly.
Otherwise, to take the filter off requires a very skinny open wrench. Not sure about the size but it's not small. You can replace the filter with a new one, but this likely is not your problem.
Once you know what the noise sounds like of the air rushing through on cold starts, you don't really need a piece of hose to hear it, you will recognize it just being close enough to the engine with the hood open.