Clay workers usually heat things up. There are exceptions, but they really are exceptional uses. In order to fully understand our processes we have to understand how things combust and what biproducts this combustion produces and at what temperatures. 

The players:
Oil, fossil or vegetable. I suppose animal oil as well.
Coal
Charcoal will be handled under wood as will sawdust
Natural Gas Methane
Propane

This paper will not be fully footnoted if it is footnoted at all. 
In order to understand combustion you really have to know something about how molecules are bonded together. Molecular bonds hold cellulose molecules together and also hold methane and propane together. Methane holds four hydrogen atoms to one carbon atom, CH4 . In order for methane to burn you have to add enough energy into the system to break the bonds between the atoms so that they can recombine to form new compounds that are more tightly bound together. Because they are more tightly bound together this releases heat. So it takes heat to release more. 

When you heat up organics bonds break. Long molecules like cellulose become shorter. Some of these shorter elements recombine to form new compounds. At low temperatures these generally do not break far enough to then burn to carbon dioxide and water vapor, although there can be some We get mostly other organic compounds. 
Initial heating up to 200˚C produces acetic and formic acid, and perhaps a small amount of carbon dioxide, glyoxal and water. Glyoxal is a dialdehyde. What happens in the next temperature zone  200˚C -280˚C is similar but with possibly a bit of carbon monoxide formed. So far the reactions are endothermic. The absorb energy. They do not release heat. 
Above 280˚C the reactions become exothermic, they release heat. You get carbon monoxide and dioxide, acetic and formic acids, formaldehyde, water vapor, methanol and hydrogen. There is also some vaporized tar.  If you hold a piece of wood at 400˚C by the time the temp has reached the center of the wood it will have stopped smoking. 

Your nose is able to detect aldehydes in very small concentrations. To my nose, most bisque kilns if the clay is not quite pure, smell like dirty vanilla. Vanilla is another aldehyde. There are some quite nasty aldehydes, formaldehyde being a notable one. acetaldehyde, and acrolein are others  It is smart to limit how much of these chemicals you breath. They can cause oxidative stress and DNA damage. Vent your indoor kilns. Its smart.

The organic acids are hard on the metals surrounding your kilns. They can eat metal roofs above kilns, remove zinc coatings,but first they generally rot the band of your kiln lid. You want these to leave your kiln as soon as possible so keep a top spy open at least before red heat, and to protect your indoor space,,,
Vent your kiln. 

Its not like you smell your kiln once and fall over dead. These chemicals are also produced by candles, incense, campfires. Gas kitchen stoves produce formaldehyde according to recent studies, but also benzene and other hazardous chemicals. These chemicals are part of the issue with cigarette smoke that makes it so carcinogenic. 

Its easiest to just look at one kind of fuel, but unless we are talking about hydrogen gas as fuel the basic principles are all the same. I like using methane, the main constiutent of natural gas that is delivered in pipes from central gas plants in the US. Methane mentioned above is CH4. Heated with oxygen it burns. If there is enough oxygen then most of what you get is CO2, carbon dioxide and H2O, water in vapor form. While a net heat is produced when the carbon and the hydrogen in CH combine with oxygen, there are two places in the process that produce losses. . One is the energy it takes to break the bonds between the carbon and hydrogen. The second is that the water that occurs is in vapor form. When it leaves the kiln and cools it condenses releasing heat as it condensces. Since it started as gases this is not really a loss in some senses but if you could condense the gas in the kiln it would release heat.