Here are some excerpts of the proposal (from page eight of the new guidelines for cleaning in New York):

1. Schools should use the most environmentally sensitive general purpose soil cleaners, carpet cleaners, and bathroom cleaners that clean effectively in cold water.
2. Hot water melts and spreads soils that are not dissolvable by water (grease, oil, fat, etc.) and those soils are likely to cling to the colder surface being cleaned, such as the carpet. If the surface is not rinsed properly before it is allowed to dry, other soil particulates in the cleaning solution will also cling to the carpet causing a "left behind soil" residue.
3. Products that have been certified by Green Seal, Inc. are designed to work with cold water.
4. Hot water requires the use of a heat source, which is a waste of energy resources.
The use of cold water saves money and reduces labor and energy consumption.

And this is from the bottom of the page, discussing extraction cleaning:

Use products with pressure-injecting and extraction machine for use on severely or deeply soiled carpets. Rotary machine brush shampooing may be performed after pre-treating and before injection/extraction. (Use of cold water for the injection/extraction process is recommended for the same reasons as with floor care – cold water pulls the soil away from the carpet fibers.)