Heat capacity
"a dielectric mineral oil blend called ElectroSafe, an electrical insulator it claims to have 1,200 times more heat capacity by volume than air"
Not really an amazing claim. Petrol has volumetric heat capacity 1,200 times higher than air, so all they're saying is that their mineral oil is, in fact, oil (specifically short-chain alkanes very slightly longer than the mainly octane and heptane in regular petrol). This also highlights why water is still the preferred substance for actually shipping the heat away with all the faff that having an extra heat exchanger requires - its heat capacity is another 4 times higher again.