Is water at the bottom of the ocean always colder than the surface water?

No. The water near the thermal vents in deep crevacis in the oceans is actually hotter than that of the surface water, but for the most part yes because the light does not penitrate that far down causing the water to be colder than the surface.

Water is most dense and and sinks at 4 deg Centigrade. Once the entire body of water gets to 4 deg centigrade if the air cools the surface water it will be less dense and float on top of the 4 deg centigrade water. Ice is even less dense and floats on top of the water.

If it weren't for this simple fact the oceans would be frozen from the bottom to the surface and only the surface would be liquid for time when the air was hot enough.

Most of the time but not always. Cold water is denser (heavier) than warm water, so it sinks to the bottom. Also the water on top is exposed to sunlight and heat, water molecules move around a bit more, have more energy, and become warmer.

In most cases yes, that is true.

There are exceptions: On the floor of the ocean there may be vents of volcanic gas. In that case the water temp will be higher around the vents.

Usually, but not always. Should there happen to be a volcanic vent on the bed of the ocean then, by that, the temperature down below could be hot.

cold water sinks and hot water is lighter in most cases but not all applications

Harlee, are you kidding me?!?! Really?!?! What if Mr. Polaski finds this on the internet one day?!?! Nex time just ask Jess or I. We would have told you!

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