The sun is just another sorce of heat. You have little or no control over the amount of heat your model recieves. If left in the sun you could end up with a plastic blob, which you almost had when you left your model to be displayed in the store window.
The warm water is a excelent idea.
I have used this mant times to straight warped parts or to stretch the sides of a body to fit over a slot car chassis.
I use hot water out of the tap to warm the body then let it cool while holding it a little past the position I need it to move to. (need to allow for a little spring back in the plasic).
This method gives a lot of control over how much heat and for how long.