Why does salt water conduct electricity best at higher temperatures?

Fact is that material or electrolite is conducting electrical current using free cariers (electrons, ions,etc.).Well, if you increse temperature of salt water number of free ions are incresed as well. Thers your answer!

The electrical resistance is also lowered by the increased kinetic energy in the solution.

Why are there more ions in heated solution?

Ok. For widther explanation you sholud get to know some more facts about conducting electrical current. I will try to explain as good as I can but I must warn you that english is not my first language. Nevertheless as I alrady mention it, current is possible couse of existance of free cariers of electrical carge (electrons and ions in most common cases) . If you bring a hit to this mixture (or to be precis energy ) moleculs of salt will brake to anIons and catIons! If you know structur of atom you shold be aware that nucleus (protons+neutrons) of any atom is surrounded by electrons wich constantly are rotating around nucleus (great speed of rotating). Electrons are located in energy levels or zones. Most of the Athoms are electricly neutral before hitting. (equal summery of positiv and negativ charge) Electrons which are farther of nucleus contains more energy then electrons closes to nucleus. If you bring some more energy to electron (by calling hit in help ) it will leave athom. That way we are getting non-neutral atoms (Ions) and free electron. If ther is an electric field whit in salt water free electrical cariers will start to move! More electrons or Ions stronger current. This is most simple explanation couse there are much more side effects which i have not considered.