NSES Content Standard B 
Physical Science: Conservation of energy and the increase in disorder
Grades 9-12, page 180

Heat consists of random motion and the vibrations of atoms, molecules, and ions. The higher the temperature, the greater the atomic or molecular motion.

Benchmark 4D The Physical Setting: Structure of Matter
Grades 6-8, page 78
Atoms and molecules are perpetually in motion. Increased temperature means greater average energy of motion, so most substances expand when heated. In solids, the atoms are closely locked in position and can only vibrate. In liquids, the atoms or molecules have higher energy, are more loosely connected, and can slide past one another; some molecules may get enough energy to escape into a gas. In gases, the atoms or molecules have still more energy and are free of one another except during occasional collisions.

Benchmark 4E The Physical Setting: Energy Transformations
Grades 6-8, page 85
Energy appears in different forms. Heat energy is in the disorderly motion of molecules; chemical energy is in the arrangement of atoms; mechanical energy is in moving bodies or in elastically distorted shapes; gravitational energy is in the separation of mutually attracting masses.

Benchmark 4E The Physical Setting: Energy Transformations
Grades 9-12, page 86
Heat energy in a material consists of the disordered motions of its atoms or molecules. In any interactions of atoms or molecules, the statistical odds are that they will end up with less order than they began--that is, with the heat energy spread out more evenly. With huge numbers of atoms and molecules, the greater disorder is almost certain.