Would a knock sensor not working properly affect running only when its 40 deg. or colder? And how can I test it to make sure if it is working?

 

I'd think that would be unlikely.

Best way: Connect a scan tool, look at knock sensor/engine timing data. Put automatic transmission in "low", foot HARD on brake, stab gas pedal momentarily with other foot. You should see the knock sensor become active, and the timing retard. If you have a manual trans, you'll have a helper watch the scan tool while you drive the vehicle. When you get to high gear, stab the gas pedal when it's safe to do so. Sudden, heavy throttle should make the sensor active.

Sorta-kinda, maybe acceptable way: Engine at normal operating temperature, idle speed. Connect timing light. Tap engine block, head, or intake manifold with a small hammer--not hard enough to cause damage. Timing should retard momentarily, then advance to "normal" with each tap.

Either way, you need to be careful. My V-6 engines have so much piston slap that the knock sensor is perpetually trying to retard timing.