Here's a distinction that trips people up: temperature is a measure of how fast particles are moving (average kinetic energy), while heat is the total energy transfer. You can have a cup of hot coffee (high temperature) that has less total heat than a bathtub of warm water (lower temperature but much more mass).
Both matter, but in different ways.
Laws of Thermodynamics
First law: energy can't be created or destroyed, only converted. Second law: entropy (disorder) always increases in an isolated system. Third law: you can never reach absolute zero.
These aren't just abstract ideas - they explain why perpetual motion machines are impossible and why cooling things gets harder the colder you go.