because cremation only uses wood like in old fashioned viking funeral pyre's eh?

I think not.

https://en.wikipedia.org/wiki/Cremation#World_War_II

The Vrba–Wetzler report offers the following description.

At present there are four crematoria in operation at BIRKENAU, two large ones, I and II, and two smaller ones, III and IV. Those of type I and II consist of 3 parts, i.e.,: (A) the furnace room; (B) the large halls; and (C) the gas chamber. A huge chimney rises from the furnace room around which are grouped nine furnaces, each having four openings. Each opening can take three normal corpses at once and after an hour and a half the bodies are completely burned. This corresponds to a daily capacity of about 2,000 bodies... Crematoria III and IV work on nearly the same principle, but their capacity is only half as large. Thus the total capacity of the four cremating and gassing plants at BIRKENAU amounts to about 6,000 daily.

https://en.wikipedia.org/wiki/Vrba%E2%80%93Wetzler_report

http://germanhistorydocs.ghi-dc.org/pdf/eng/English45.pdf