The temperature of a gas is equal to the translational kinetic energy of the average molecule in that sample.
The heat content of that sample of gas is the sum of its energies, internal and external, except nuclear energy, of all its molecules.
The term, translation, means motion of the molecule as a unit.
An increase of one degree Kelvin or Centigrade is the additional translational kinetic energy received in the process. It is a standard quantity, and it is the same for each rise of one degree at any temperature.
To arrive at the standard degree, one finds the energy of the average molecule of air at the freezing point of water, and the energy at the boiling point of water. Subtract the smaller figure from the higher number, and divide by 100.
One might wonder how air, which contains various molecules of vastly different molecular weights, can have the same average kinetic energy for all. The answer is that lighter molecules move faster than heavier molecules. A slow-moving heavy molecule can collide with a stationary light molecule, and cause the light molecule to move at a much greater speed than the heavy molecule had before impact.
The internal energy of a molecule consists of the motions of the nuclei and electrons of the atoms of the molecule. The motions of the nuclei are not to be confused with nuclear energy, which is inside a nucleus.
When a molecule collides with another, it forces the nearest part of the molecule to move toward the rest of the molecule. The interaction forces cause the atoms to rebound. There ensues a series of bounces or oscillations which become part of the internal energy of the molecule.
In the air at room temperature hardly any time passes between collisions. In every collision there is a transfer of energy in one direction or the other. For example, a molecule may enter into a collision at just the instant when its oscillating atom is swinging outward. The motion of the atom plus the motion of the molecule add up to a lot of energy to transfer.
The concept "temperature" is independent of the quantity of matter. Even a single molecule has a temperature according to its translational energy. However, the concept "heat" involves the quantity of matter. There is "specific heat" which is the quantity of heat gained by a gram of a substance as its temperature rises one degree. Then there is "heat capacity" which is the heat gained by one molecule of a substance as its temperature rises one degree.
Different substances at the same temperature have different quantities of heat per molecule or per gram.
One of the characteristics of a molecule that contribute to its heat capacity is the number of ways that its parts can oscillate. An outstanding example is the molecule of carbon dioxide. It consists of three atoms in a row, with the carbon atom in the middle, between two oxygen atoms. The molecule can rotate like a revolving door. Each oxygen atom can oscillate away from the center and toward the center. Or else the oxygen atoms can jump up and down in unison, while the carbon atom oscillates down and up to compensate, and keep the center of gravity comparatively still.
It is this quality of the carbon dioxide molecule that makes it a candidate for greenhouse gas. Sunlight passes through the air easily, if not perfectly. The sunlight warms the ground and the oceans. Some of the heat in the ground returns as infrared radiation; and some frequencies of infrared match the oscillation fequencies of carbon dioxide molecules. The heat that is absorbed by carbon dioxide is shared with air molecules via collisions.
The case against carbon dioxide is not easily established. The percentage of air molecules that are carbon dioxide is a small fraction of one percent. That much carbon dioxide has always been there. It is claimed that atmospheric carbon dioxide has doubled. Even so, it is still a small fraction of one percent.
Carbon dioxide is essential to plant life and growth. It is consumed by seaweed. It is easily dissolved in water. It reacts with water to form carbonic acid.
It is very difficult to discover whether there is a warming trend in the climates of the earth. The quantity of matter in the atmosphere is less than the matter of the surface of the continents and very much less than the matter in the oceans.
Even if the average temperature of the atmosphere goes up, and the glaciers melt, that is only temperature. A much more significant factor is heat. Water has a higher specific heat than most substances. How can we get a significant figure for the heat content of the oceans?
One more consideration is the clouds. Clouds are very effective reflectors of sunlight. If more heat occurs in the oceans, there will be more evaporation and cloud formation, therefore more reflection of solar radiation.
The sun is not the only source of heat. There is enough heat in the earth's core to move continents. Some of that heat reaches the surface steadily, and some arrives sporadically. There is no way to predict the next outburst of enough heat to alter the climate.
In the recent past there was a volcanic eruption that discharged enough dust into the upper atmosphere to interfere with the arrival of solar radiation. One effect of this was to alter the climate for several years, lowering the average temperature.