I recently ordered a Xeon E3-1265L v2 CPU to replace the stock Intel Celeron G1610T in the Gen 8 Server.
These processors have much better performance and cost a lot less now so definitely worth looking into.
I followed the steps in the Official Maintenance and Service Guide PDF below: HP ProLiant MicroServer Gen8 Maintenance and Service Guide
The Intel ARK website details the specs of the 2 processors:
Intel® Celeron® Processor G1610T
Intel® Xeon® Processor E3-1265L v2
This is also a good time to clean out any dust inside and outside the case
Arctic MX-4 Thermal Compound added to Xeon Processor 
Motherboard placed back inside case
I connected everything back up then accessed the iLO to check the Processor was detected. I had no issues at all and the VM’s all worked as normal after the upgrade.
I upgraded the iLO and BIOS as it was 2 years out of date.
iLO 2.73 download page
I extracted the self extracting exe and used the bin file to flash the firmware inside the iLO interface.
The new iLO has a much better HTML 5 Remote Console compared the the previous .Net and JRE based ones.
The BIOS was done in a similar way by flashing it in the same firmware interface then switching on the server and following the on screen instructions.
BIOS J06 04/04/2019 download page
Hello, i used to do the same upgrade as you, in the bios options do you put the Intel Turbo Boost Technologie on ?
What is the HP Power Profile you take ? Balance Power and Performance or something else ?
And about the Thermal configuration, are you keeping the Optimal Cooling or change it ?
I think this processor is not making too much heat… so i keep the default heat sink i guess you do the same ?