Temperature and Heat

Thermal Energy 

   Thermal energy comes form the movement of atoms and molecules in matter. It is a form of kinetic energy produced from the random movements of those molecules

How an atoms expresses this kinetic energy is in several ways. 

1. Random Linear Motion- like billiard balls bouncing around on a pool table.

2. Random Rotational Motion- molecules spinning about tops 

3. Random Vibrational Motion- Like two masses attached to a spring. 

Temperature 

 While temperature is related to thermal energy, there is no absolute correlation between the amount of thermal energy (heat) of an object and its temperature. Temperature measures the concentration of thermal energy in an object in much the same way that density measures the concentration of matter in an object. As a result, a large object will have a much lower temperature than a small object with the same amount of thermal energy. Also different materials respond to changes in thermal energy with more or less dramatic changes in temperature

        Definition provided by school of champions

Heat

   Heat is a measure of how much thermal energy is transmitted from one body to another. We cannot say a body “has” a certain amount of heat any more than we can say a body “has” a certain amount of work. While both work and heat can be measured in terms of joules, they are not measures of energy but rather of energy transfer. A hot water bottle has a certain amount of thermal energy; when you cuddle up with a hot water bottle, it transmits a certain amount of heat to your body.

Definition provided by Sparknotes

 Difference Between Heat and Temperature

 In our everyday vocabulary we tend to use the words "Heat" and "Temperature" interchangeable, but they mean very different things. 

   Temperature is an expression of the average kinetic energy an object has.  Now depending on that objects composition and phase has a major effect on how that kinetic energy is expressed. 

    Heat on the other hand is the amount of energy being transferred from one object to another. No mater what that object is our how much of matter it has the Heat would still be the same.

So when thermal energy is transferred to one object to another it's "Heat", where Temperature is an expression of how much kinetic energy an object has. 

Thermal Energy is not Total Energy 

   In a closed system we know that energy is conserved, that is kinetic and potential energy of a system can grow and shrink, and in some cases even negative.  

    The first law of thermodynamics restates conservation of energy.  If a system is closed, in thermal physics we refer to as isolated, that energy may transform from mechanical to thermal to chemical to solar but the total amount doesn't change, so if thermal energy is molecular motion basically kinetic energy, is there a molecule potential energy we should concern our self with? 

   In chemistry a considerable amount of time is spent talking about "bonds", whether the bond is atomic, primarily electrons to the nucleus, or inner molecular, atom to atom bonding, or even extra molecular bonds, each of these bonds represent a form of potential energy. 

   In phases of matter we spend some time on how this energy is expressed in form of matter.