^ That is correct. The inverse is also correct. Coolant (not water), together with pressure, raises the boiling temperature of the coolant/water mixture in the radiator. But coolant is also poorer at holding heat. Water by far has better heat holding ability. Running straight water will actually make your engine run cooler. But you don't want to do that because adding coolant increases boiling point, prevents freezing, and has corrosion inhibitors to protect aluminum and other engine parts (i.e. pump, gaskets, hoses). Water will straight out eat into aluminum and rust out the iron in the engine.

During early morning startup, the coolant mixture actually helps the car warm up faster and helps get the ATF flowing to its operating temperature around the cavities, passages and solenoids of the AT housing. Shifting immediately before the ATF is warm can usually lead to shift delay, shift shock and/or harsh shifting, particularly with older vehicles.