What is the best way to measure temperature in a swamp cooler?

Cold water alone will not drop your temperatures eight degrees. You will need ice packs. A more readily available option is to go out and buy a case of water bottles from the store, freeze a couple of bottles, and just rotate them out every 6-8 hours by placing them in the water of the swamp cooler. Take an old cotton t-shirt and pull it over the top of the carboy/bucket, and set up a small fan to point at it on a low speed to try and slowly dry out the shirt, allowing it to wick up more water. This should get you down to the temperature you need.

For measuring temperature, get a stick-on thermometer strip to place on your carboy/bucket. The way you'll want to do this is to make sure there's enough of a gap between the water line of the swamp cooler, and the top-off line of your carboy/bucket to place the strip (horizontal would be ideal). In this gap, place your thermometer strip, that way it isn't measuring the temperature of the water in the bucket. The beer will ferment at a higher temperature than it's ambient surrounding temperatures, therefor it isn't accurate to measure the water temperature, since it will be lower than the beer.

Alternatively, I've heard great things about cool-brewing.