Heat isn't temperature

I probably need to get this out of the way, too.

These words are often used interchangeably in everyday communication, but they are quite different from each other in the energy world. Heat is a form of energy, similar to kinetic energy. Temperature is something more like the concentration of the heat.

Kinetic energy is the "energy of motion" that all moving objects have. The faster a given object is moving, the more kinetic energy it has. When you stop a car by using the brakes, all of the kinetic energy gets converted to heat in the brake discs, in a controlled way. Doubling the speed actually increases kinetic energy by a factor of four, which is why it takes so much longer to bring a car to a stop from a higher speed. In a car crash, the kinetic energy gets converted to heat in an uncontrolled way, causing destruction of bodies and bodywork in the process. 

Kinetic energy depends on mass, as well as speed. A heavier car has more kinetic energy than a lighter one, travelling at the same speed. In fact, a car that's twice the mass will have exactly twice the kinetic energy at the same speed as the lighter one.

Heat energy is actually the kinetic energy of molecules - the individual building blocks of matter. Temperature is something like the speed of the molecules. So temperature and heat are different, in the same way that speed and kinetic energy of a car are different. Higher temperature means more heat energy, but more mass (ie, more material) also means more heat energy. A cup of hot coffee represents a certain amount of heat energy, two cups of hot coffee (same mass, same temperature) contain exactly twice as much heat energy. 

You can verify this in your kitchen fairly easily. Your kettle converts electrical energy to heat energy at a particular rate (corresponding to its power rating, usually 2200 watts or so). So 2200 watts, multiplied by how long the kettle is on, quantifies how much energy is converted from electricity to heat. You'll find that, starting from room temperature, boiling twice as much water takes about twice as long, at that constant energy transfer rate of 2200 watts. (It won't be exact, because there are several other minor effects going on as well, such as the time it takes the kettle to click off, after the water has boiled).

I mentioned that temperature is like the concentration of heat. Concentration is important, because "stuff" naturally wants to flow from high concentration to low. Fluids flow from high pressure to lower; electricity flows from high voltage to lower; and heat flows from high temperature to lower. Heat and temperature aren't the same thing, but they are both important because temperature tells heat how to move. The way that heat moves is a critical to understanding important parts of our energy system.