Basically, heat is energy. It manifests itself as either molecular vibration within a substance or as an electromagnetic radiation. Temperature on the other hand, is simply a measure of the amount of heat present within a material.
Units of Measure
As energy, heat is measured in watts (W) whilst temperature is measured in degrees Celsius (°C) or Kelvin (K). Sometimes the term absolute temperature is used to denote that it is given relative to absolute zero - the point at which an object contains absolutely no heat energy.
This occurs at -273 °C or zero Kelvin (K). The Kelvin scale is equivalent to Celsius in every way except that it begins at absolute zero whereas the Celsius scale begins at the freezing point of water.
Heat Flow
The second law of thermodynamics states that energy (heat) transfer can only take place in one direction, from a higher grade to lower grade state. This means that heat will only flow from hot to cold, never the other way. The tendency will always be towards an even distribution of heat energy within any environment such that, with no additional heat input, all objects will eventually end up the same temperature. Heat flow between objects occurs in three ways.
Conduction
This form of heat propagation results from the transfer of vibrational energy from one molecule to the next. When an atom begins to vibrate, it generates an electromagnetic field that interferes with the electromagnetic fields of surrounding atoms. This interference occurs in the form of an energy transfer. The closer together the molecules of a material, the greater the interference and the faster the heat transfer rate. The heat flow rate is referred to as the conductivity of a materials and tends to be greater in high density materials.
The rate of heat flow from one side of an object to the other, or between objects that touch, depends on the cross-sectional area of flow, the conductivity of the material and the temperature difference between the two surfaces or objects.
Convection
Heat transfer from a solid to a fluid (liquid or gaseous) is more complex than solid-solid transfer as heat differentials within the fluid generally cause internal movement known as convection currents. As volume increases with temperature, warmer areas of a fluid have less mass that colder areas.
The force of gravity causes the denser material to displace the lighter material, thus forcing it to rise. The magnitude of convective heat flow within the fluid depends upon the area of contact with the solid, its viscosity, velocity past the solid, flow characteristics and the overall temperature difference between the two. The term convection has also been used historically to describe the transport of heat from one solid to another separated by a fluid medium.
Radiation
Radiant heat is simply heat energy in transit as electromagnetic radiation. All objects that contain heat emit some level of radiant energy. The amount of radiation is inversely proportional to its wavelength (the shorter the wavelength the greater the energy content) which is, in turn, inversely proportional to its temperature (in °K).
Hence, objects at terrestrial temperatures radiate long-wave infrared whereas very hot objects, such as the Sun, emit both long and short-wave radiation.
Summary
The most efficient method of heat transfer is conduction. The transfer occurs as the fast-moving molecules of the hot object bump into the slower-moving molecules of the cold object. The fast molecules give up some of their energy, slowing down, and this energy goes into speeding up (and thus heating up) the slow molecules. The exact speed of this transfer therefore depends on the molecular density of each material. Metals, being quite dense, are the most effective heat conductors whereas gasses are among the worst.
A slower method of heat transfer is convection, which occurs in fluids or gases. A cool fluid in contact with a warm solid will heat up through conduction. As it heats, the fluid will expand slightly and its density will be reduced. As the warmer fluid is in contact with the cooler fluid, the weight of the cooler section of fluid forces the warmer section to rise, setting up a convective current. Because material must actually be moved, convection is less efficient than conduction.
The least efficient method of heat transfer is radiation. In this case, heat moves through space as an electromagnetic radiation without the assistance of a physical substance. This is how the Sun's heat reaches the Earth. Radiative heat is transferred directly into the surface of any solid object it hits (unless it is highly reflective), but passes readily through transparent materials such as air and glass.