P20 is a designation used in ASTM A 681.  The UNS designation is T51620.  Equivalent grades to consider checking out:
DIN 1.2311, 1.2328, or 1.2330
BS 4659 (USA P20)
AFNOR A35-590 2333 35CMD7

Density is 7.85 g/cm^3 (according to ASM HANDBOOK Vol. 1)

I could not find anything on thermal conductivity or specific heat.  I am guessing you need this to perform some type of engineering analysis (FEA, solidification analysis, etc.).  You may try one of the software vendors to see if they have this in their database-- it is a very common steel grade used in the injection molding industry.

Based upon P20 composition, you could estimate the heat capacity and thermal conductivity by using the values for SAE 4140 steel.  Matweb has these properties, but beware that they are not constant, rather they vary with temperature.  Using software with an internal database would be a wise choice.

My olde Crucible Data Sheet (circa 1985) on their CSM 2 ® tool steel (AISI P20) gave the following:

Specific Heat, BTU/lb/°F, from 122 to 212 F was 0.114

Thermal Conductivity, BTU-ft/hr-sq ft-°F, 200°F was 24.7       400°F was 27.5

Density , lb/cu in was 0.284

Of course, this is all on the prehardened, as received tool steel.  Remember that P20 is often used carburized, and hence your properties for the case may very well be different.

Good luck!

Lee

I am loking for any information on PGK grade tool steel.  I have never heard of it and needed to learn more about it.  Thanks