I have tried to stay away from this thread, but there is just so much missunderstanding that some of the record needs to be put straight.
First of all, PCB is not "highly carcenogenic". There are about 110 different ways to attach more than one chlorine atom to a biphenyl molecule, and of those fewer than 12 are "suspected" carcinogens. Almost anyone my age from the electrical industry can tell you endless stories of cleaning their tools and hands daily for years in the stuff, and about the only reaction has been mild skin irritation in some cases. However, it IS incredibly persistant and once it is "in" you, it isn't going anywhere for the rest of your life, so the last thing I recommend is going out and using it for cleaning solvent or salad dressing.
The problem with PCB from a testing standpoint is that congenor specific analysis is AES, mass spec or similar and costs so much that it is cheaper to just treat the whole thing as carcinogenic and measure concentration with GC. Costs less to just buy new oil.
The requirement for thermal destruction (there are several other ways - but mostly chemical reaction with sodium) is a minimum of 1,100 deg. C with residence time of at least one full second in an oxygen rich environment to reach the EPA standards for destruction. It shouldn't take a math major to figure out that those conditions are NEVER met inside of an engine. Do anything less, and you do just what others have mentioned: you make di-furo benzines (furans) and those ARE incredibly carcinogenic.
There are several different ways to make insulating fluids used in high voltage electrical devices. Most use napthenic base stocks, increasingly more use Group III (severely hydrotreated) parafinnic base since napthenic crudes are getting harder to come by every year, some use synthetic asphaltenes, some use bio-base (soy) oils and some are silicone compounds.
Believe me when I tell you that anyone in the industry knows EXACTLY what material they are handling. Older equipment (lots still around) may well have been remediated to some level (50ppm in service in some places, usually <2ppm for transportation as non-hazmat up here, not sure of US limits). NOBODY will put anything into their equipment (processing) without a clear chain of custody from sampling to an independant lab analysis. Contaminants in the parts per BILLION can affect surface tension enough to make the fluid un-processible. Silicone is a HUGE contaminant to petro (and bio) fluids as it is a common and powerful surfactant. In today's highly litigous and insurance-dominated business, PCB contamination at ANY detectible level (now down to 0.1ppm for most competent GC labs) won't be tolerated. The financial risks are just too high.
The business of PCB being "in" the transformer (old ones) is quite correct. When such units were flushed many years ago to be classified as "PCB free", there was (is) no way to get the oil that impregnates the insulating system (essentially kraft paper) out, so the rule of thumb was that a unit would "leach back" to 10% of its previous PCB level (usually starting at 40-60%) over time, so anything from an old unit is always highly suspect. Most have been flushed twice to be around today. The big risk is not large transformers (5,000 gallons is actually on the small end, most are designed with fluid capacities in MULTIPLES of 5,000 USG since that is one 5 axle load) since everything about them is HIGHLY monitored. It is the little padmounts and poletops that are usually loosely followed. That is why nobody in the used oil business will touch a drop of transformer oil without testing FIRST - and even then only from a known and trusted source.
While it would be nice to think that this stuff is treated royally in the post-first-use stages, in fact the majority will end up as fuel in cement kilns or asphalt paving heaters. It is highly prized for that, and I am disturbed to the limit on thinking that there is 50ppm stuff in the US (NOT happening in Canada, because you can't haul it without registering as hazmat) that sees this use. Obviously anything above that level SHOULD be getting proper treatment (but by the sound of some of these posts, it obviously is NOT). Unfortunately, the old saw still applies to many generators of used oil: "the solution to pollution is dillution".
As far as getting out of a transformer into the waste stream: modern transformers do not typically "breathe" to the atmosphere at all. The oil remains dehydrated and degassed under a diaphragm. When it DOES accumulate sufficient gasses and water (that is in a few parts per MILLION of water...far, far dryer than what we get at the pump) it is mechanically processed to remove them and circulated back into the unit without ever being exposed to air. It is NOT highly formulated (i.e. has very few additives) and MOST (i.e. napthenics) are treated with 0.07% (IEEE Type I) or up to 0.3% (Type II) DBPC - ditertiary-butyl-para-cresol - that is an antioxidant found in diesel. The life of insulating fluids is closely monitored, and in large units, once the inhibitor is seen being used up, it is usually re-inhibited and processed, not disguarded. In extreme cases (some moron did not sample for a VERY long time) it is treated by adsorption to remove polar compounds, re-inhibited and re-used.
What I am saying in that rather long diatribe is that there are usually only two reasons that oil is being removed: from a large unit - it has failed or reached end of life and is coming out of service or the utility has accumulated a lot of small bits from little transformers and it is too badly contaminated to be used. These are both VERY HIGH RISK situations since we are now talking about old stuff that might have been around since before the war.
As far as burning in a diesel: while there is no doubt the engine will run, the story for this, lubricating oil, or a host of other stray formulated petroleum hydrocarbons is that the additives are not necessarily what you want in the engine, and the contaminants are a crapshoot at best. Also, what makes you think you are getting the relatively burnable base stocks instead of asphaltene or silicone contaminated JUNK oil (as I hope I have pointed out, if YOU are getting it, it is NOT from the highly controlled part of the business).
In summary: unless you know EXACTLY what you are doing and what you are handling, only a fool or a pro will even THINK of dealing with this stuff.