When an object is tidally locked, that means its rotation period is the same as its orbit and always has the same face towards its parent body. Our Moon is a good example of this.
What you described with one side (the lit side, not neccesarily its south pole) being a scorching desert and the other side (the permanent night side) a frozen wasteland with the regions in the middle being habitable is a pretty good description of what can happen to a tidally locked planet. Although in thinking about it, what you're describing could be more like a situation with a 90 degree or near 90 degree axial tilt.
However, when you add an atmosphere and depending on the properties of the planet itself (how much water it has, etc), things become more complex. A high axial tilt would make it difficult for life, but not impossible, same with a tidally locked world. There are others who can probably expand on this better than i can.