In a heating curve, when is the temperature constant?

The temperature is constant when the line is horizontal (flat).

When the line is flat, it means that the temperature is constant and also that the phase is changing. A good way to think of this is flat lines imply the heat isn't increasing or decreasing. The slope of a flat line is 0 meaning it is constant. So as time goes on, the temp stays the same.

When a substance is changing phases, it is gaining phase energy. At DE and BC the temperature is constant since it is changing states. For Example: at BC substance is changing from a solid to a liquid.

Check this video out for more info on heating and cooling curves.