How can I check to see if they are working properly?

 

There are technical ways to check these items, but for the sake of ease this is what I would look for:

Fan control switch- I would just wait for the car to warm up 10-15 mins and see if fan turns on. Both fans should be running with A/C on.

Thermostat- Car should warm up within a few minutes of driving and not pass the halfway mark on the temp gauge. Also, temp gauge should not go down when cruising on highway or in cold weather condition.

 

Excellent!!! Thanks! I'll have a look-see