Which of the properties of water would be most important in protecting a fish in a shallow pond on a hot summer day?

Probably water's high specific heat.

I teach my Biology classes about some of the weird properties of water:

It has a high Specific Heat, a High Heat of Vaporization, it is less dense as a solid, and so on...

A good "layman's definition" of specific heat is the amount of heat needed to raise the temperature of a given substance. (A good scientific definition would be a bit more precise) Because water contains an extraordinarily high number of hydrogen bonds, it takes a lot of energy to change the temperature of water. In the case of our marine friend in the example above, that will be very advantageous to his life! Why? As water heats up, it has a harder time holding onto the oxygen dissolved in it. If the pond gets hot enough, the fish in it can suffocate.

Sadly, I watched this first hand in the lake behind my house. Last year here in Texas we had some record heat and droughts. Many of the fish in the lakes died as a result.

The same thing happened to the fish in the Delaware Bay, if I'm not mistaken.