Here is some comparative information I derived using the Heat Convection and Conduction formulas:
NOTE: This was for

pure mineral oil verses

pure PAO synthetic both 10.5

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Convective Calc:
H = F.rho.c(To-Ti),
where H is heat energy in Joules, F is volume flow in cubic meters/s,
c is heat capacity in Joules/kg.C, and temps in C. The c for synthetic oil is 2000 J/kg.C and c for dino is 1780 J/kg.C. I assumed a flow rate was 1/4 liter per second, To is temp out of a journal bearing = 100 C, and Ti was oil temp into bearing = 80C, representing a temp rise of 20C, which is a rule of thumb.
Hs = convective energy transfer in Joules for synthetic = 10.65 J
Hd = convective energy transfer in Joules for dino (mineral oil) = 9.3 J.
Therefore, pure synthetic oil is 13% more efficient at convective heat transfer.
The "rho" factor (oil convection heat transfer) is the oil's density, measured in kg/cubic meters, and since both oils were so close in density, I used 1.065 kg/cubic meter.
Using the

Heat Conduction formula:
H = kA(To-Ti/L),
where H is heat Power in W.m, k is heat conduction coefficient in W/meter-squared/C, and temps in C. The k for synthetic oil is 0.16 and k for dino is 0.128, To is temp out of a journal bearing = 100 C, and Ti was oil temp into bearing = 80C, representing a temp rise of 20C, which is a rule of thumb. L is the thickness of the oil film which is on the order of 1um at high loads. A is area of film assumed to be a patch of area of 1 mm squared.
Hs = conductive heat transfer of synthetic oil in W = 3200 W,
Hd = conductive heat transfer of dino (mineral oil) in W = 2560 W.
Therefore, pure synthetic oil is 20% more efficient at conductive heat transfer than mineral oil.
The same film thickness for both dino's and synth's were used for the calculations.
These are heat transfer formulas from thermodynamics and the constants I used for "c" and "k" were from Michael J. Neal's, The Handbook of Tribiology.
(From BITOG 07/02)