We all know that the ambient temperature (the typical temperature outside) changes throughout the day, and that the sun is responsible for generating most of that heat. But that's not because the sun is changing its temperature.

The temperature of the sun is about constant. So why does the ambient temperature change? Mostly because of angles. Think of the sun as a heat source, like a campfire or a heat lamp, except the sun is 100,000 miles away from the Earth. The part of the Earth that faces the sun receives the most heat. So as the Earth rotates, different places receive the highest amount of heating (middle of the day) and the lowest amounts of heating (middle of the night).

(Actually, the sun is slowly getting hotter, but we would only be able to notice the change over billions of years!)

The sun itself does not change temperature, but the surface of the Earth does. Temperature on Earth usually peaks in the afternoon and is at a minimum at dawn. The exact details that you ask for depend on a huge number of factors including geography, season, humidity, etc., so I can't so easily answer your second question.