Seems unlikely you will get the full 40W out from an EFD20 core without a very high temp rise: -
if you know the current wave shapes at a fixed operating point you can then compute the rms values and knowing the wire resistances at 20 deg C ( x 1.25 for 80 deg C )
you can compute the "DC" losses in the wires
as to the core - I can tell from the specs given that it is a CCM design at full power - the sec side current ripple is 6.65 A peak, 3.35 A trough
and the current ramp down ( assuming 5v5 load - i.e. diode ) takes 1.33uS, leaving ( 130kHz = 7.69uS ) 6.36 uS for the current to ramp up on the driving pri side
for the same change in energy ( increase this time ) on the pri side ( 338uJ ) and an average I in of (( 8 x 5.5 ) x 0.9 eff ) / 20 V = 2.45 A
We can see the current change in the pri side at full power is (( 5.81 A )^2 - (( 0.0 A )^2 ) x 20uH x 0.5 = 338 uJ
Lets just check if we can ramp to 5.81 amps in the time avail at low line: V/L = di/dt = 20V / (20uH x 5.81 A ) => 5.81uS so we are just OK
We can now compute the flux ripple in the core and hence the watt losses in the core as you requested:
dB / dt = V / (N . Ae ) so for 20 V in, dt = 5.81uS, N = 12 Turns and Ae = 31mm^2 ( data sheet ) we get Bpk = 312 mT, and delta B @ 130kHz = 156mT
from the data sheet for 3F3 material the supposed losses @ +/- 156mT & 80 deg C are then about 400mW per cc of core material ( 1.46 cc for EFD20 )
giving: 600mW core losses - which is getting up there for an EFD20
when we add in the wire losses for this design at full power we see that the temp rise could easily get to 80 deg C or more in an enclosed environment - and possibly thermally run away if we go over 110 deg C absolute ( 3F3 properties )
To finally answer your question - it depends on the materials used and if full power is really required - but 100 deg C abs max is a good absolute upper limit.