First off, let me say you're actually pretty lucky to broach this topic here than just googling it because the issue of the fuel used during the Holocaust is a staple of Holocaust denialism. In short, denialists argue that the Germans lacked the fuel to cremate the numbers of Jews and other victims of the Holocaust, which is an absurd claim but one that makes it a little difficult for historians to analyze the actual problems mass cremations posed for the Third Reich.

The mass murder of Jews meant that there was a logic that compelled the SS to turn to mass cremation. The SS initially used mass burial which posed a number of hygienic problems. Leon Feldhendler, a witness of the killings at Sobibor recounted:

In the first period, there was no crematorium. After gassing, the people were laid into the graves. Then, out of the soil, blood and a bad odor of gas began to surface; terrible smells spread over the whole camp, penetrating everything. The water in Sobibor became rancid.

The problems of Sobibor were similiar in many of the other death camps as the summer of 1942 was quite hot and the corpses swelled in the burial pits, spreading disease and creating a noxious environment. These early cremations used both coke fuel and wood for fuel, but were inefficient.

The solution to the SS's problem came from a number of sources. Himmler had tasked SS Standartenführer Paul Blobel in early 1942 to eliminate all traces of mass execution in the Soviet Union. The operation, codenamed Sonderaktion 1005, sought to find the ideal and practical technical solutions to the problem of mass disposals. Blobel's team experimented with various methods at Chelmno and eventually found the ideal method was to stack alternating layers of bodies and fuel connected by railway ties. One particularly gruesome discovery of Sonderaktion 1005 was that human bodies acted as their own fuel, provided they were efficiently stacked. Yechiel Reichman, a Jewish inmate at Treblinka testified postwar:

The SS “expert” on bodyburning ordered us to put women, particularly fat women, on the first layer on the grill, face down. The second layer could consist of whatever was brought—men, women, or children— and so on, layer on top of layer. . . . Then the “expert” ordered us to lay dry branches under the grill and to light them. Within a few minutes the fire would take so it was difficult to approach the crematorium from as far as 50 meters away. . . . The work was extremely difficult. The stench was awful. Liquid excretions from the corpses squirted all over the prisoner-workers. The SS man operating the excavator often dumped the corpses directly onto the prisoners working nearby, wounding them seriously.

Feldhendler similarly testified that the open-air cremations came from the problems of mass burial, which

forced the Germans to build a crematorium. It was a large pit with a roaster above it. The bodies were thrown on the roaster. The fire was ignited from beneath, and petrol was poured on the corpses. The bones were crushed into ashes with hammers.

This lesson that the disposal process was more efficient with more bodies became very important for camps with more permanent crematoria.

Both Dachau and Buchenwald had already installed their own crematoria in 1939. Although not death camps, these unhygienic conditions and general brutality created a large number of deaths among the inmates. The SS had previously farmed out these corpses to local crematoria, but the scale overwhelmed these local businesses and the SS realized that these corpses posed a public relations problem. The SS subcontracted out to two private contractors, Heinrich Kori GmbH and Topf & Sons, to create efficient crematoria suitable for mass burnings. Primarily utilizing coke for fuel, these crematoria used a variety of existing and novel technologies to recirculate heat. As Blobel and his team discovered, human bodies could act as their own fuel and their experience disseminated back through the SS's camp administrators. For example, Auschwitz's crematoria teams would mix fat and emaciated corpses together to create an even heat. The Germans constructed these permanent crematoria at the larger KL work camps and at Auschwitz-Birkenau, which began as a mass-labor camp but transitioned into a hybrid work-extermination camp as the Operation Reinhard camps wound down their operations. Kori and Topf also developed portable oil-fired ovens that could be sent to the areas needing quick disposal.

Although these mass burnings used both wood, oil fuel, and coke, only oil was in truly short supply in the Third Reich during the height of its mass disposal efforts (1942-43). The cremation pits of the Reinhard camps were located in largely wooded areas in Poland, so this fuel was readily available. The permanent crematoria were often closely connected to the SS's use of slave labor for industrial enterprises, making their supply of fuel such as coke much easier. The diabolical calculus the SS discovered was that a sustained effort of mass murder rendered this disposal process much more efficient. The victims' own bodies became a vital component of the Third Reich's attempt to dispose of the evidence of its own crimes.

Sources

Arad, Yitzhak. Belzec, Sobibor, Treblinka The Operation Reinhard Death Camps. Bloomington, Ind: Indiana University Press, 1999.

Guṭman, Yiśra·el. Anatomy of the Auschwitz Death Camp. Bloomington u.a: Indiana Univ. Press, 1994.

Wachsmann, Nikolaus. KL: A History of the Nazi Concentration Camps. New York : Farrar, Straus and Giroux, 2015.