It was an alternate universe.
The girl was Ushio and the robot was Tomoya.
And what I managed to understand was this:
Warm: Meaning Happiness, Joy, etc (A "Happy" place)Cold: Meaning Sadness, Despair, etc (A "Sad" place)Tomoya is depicted as a robot because of a robot's inability to "feel". And as you could see.....
They were in a "cold" world. Since Ushio was just represented by an older version of her. The "cold" slowly began to take her life away. Tomoya, being a robot, couldn't "construct" the perfect "object" (or building, I had no idea about what that thing was to be honest) to take Ushio and him to a "warmer" place.That's pretty a summary of what I believe it meant.