The SKF 388 steel looks to be similar to the Ladish D-6A alloy, which is listed by ASM Metals Handbook, Volume 1 as a medium carbon, ultra-high strength steel. The nominal chemical composition is listed below;
C 0.42-0.48%
Mn 0.6-0.90
Si 0.15-0.30
Cr 0.9-1.20
Ni 0.4-0.7
Mo 0.9-1.10
V 0.05-.10
If you have access to ASM Handbook, Vol 1 it contains an excellent write-up on this material, including recommended forging temperatures. It is recommended to heat this material to 2250 deg F max, and finish forging at or above 1800 deg F. Slow cool in a furnace or insulating medium.