(So I misread the first post and described many different characters, so this is an edit.)
Well, seeing as I'm Cirno's writer, I've actually given some thought to this.
Cirno's power does not allow her to heat things up. Heat is simply a measurement of energy in atoms of an object caused by vibrations. More heat = more vibration. Cold isn't a physical existing object - it isn't made up of matter.
Cirno can decrease the rate of atomic vibration, changing the state of matter from a solid to a liquid. She cannot, however, speed up this process, so if she were to freeze a lake or chill the atmosphere, she would have to wait for it to thaw or heat up.
She can, however, manipulate ice physically - moving it, breaking it, expanding or contracting it. She can shape it to her will. This allows her to build small to medium-scale constructions, such as bridges, shelter, or tools. The atmosphere contains humidity, so she has a near limitless supply of ice for her to use. In dry places such as deserts, there would be less, but as Gensoukyou does not have any deserts, it is unlikely she'll encounter a lack of humidity.
She can also manipulate cold - although has less power over it than ice. She can cool down hot objects, keep herself cool in hot places, even sufficient enough protection from the heat of places like the nuclear reactor (although the radiation could still harm her).