To cycle the tank is to let the beneficial bacteria grow in the filter (and less so in the substrate and on decorations) that will convert ammonia from fish waste into the less toxic nitrite, and then to the even less toxic nitrate, which is then removed by plants and regular water changes. The cycle won't start without an ammonia source, so just running the tank by itself doesn't do it--you either start with fish, or with straight ammonia (fishless cycle). With how long you've had the tank, you're probably pretty much cycled, but without testing it, there's no way to know for sure.
The petstores will carry test kits--strips are almost useless but better than nothing; the liquid reagents are much more accurate and worth the extra initial pay out since they last much longer than strips.
Any pet store, or even walmart usually, will carry a cheap aquarium thermometer that uses a suction cup to fasten to the glass, or you can spend a bit more for a magnetic type or a weighted type that will sit on the substrate, depending on your aesthetic preferences.
It's possible the fast (and more than two or three degrees in a day can be fast for fish) increase in the temperature shocked them, or you got an ammonia or nitrite spike for some reason--if a fish vanished, that could cause it if he's dead.
What kind of fish do you have in there, and why are you using aquarium salt? That's ideally saved for certain illnesses, and many species are incredibly sensitive to it, especially if you added too much at one time.