In this case, what I would recommend is an engineering review of the PWHT parameters to be provided to your client;
Typically, for P-No 1 base material, PWHT is not required unless forming strains have been performed or it is required by the client, if using ASME Boiler and Pressure Vessel Code, Section VIII, Div 1. If using ASME B&PV Code, Section VIII, Div 1, Table UCS-56, the PWHT temperature range for P-No 1 base material is 595 deg C or 1100 deg F minimum.
The PWHT hold time is also in Table UCS-56 and stated as 25mm thickness/1 hour or 1" thickness/1 hr. So, for a plate 13mm in thickness, if PWHT is required by your client, the minimum hold time at 595 deg C or 1100 deg F and would be 30 minutes at PWHT temperature.
The heating and cooling rates shall be based on the following requirements in UCS-56 below;
UCS-56
(2) Above 800°F (425°C), the rate of heating shall
be not more than 400°F/hr (222°C/h) divided by the maximum
metal thickness of the shell or head plate in inches,
but in no case more than 400°F/hr (222°C/h).
(5) Above 800°F (425°C), cooling shall be done in a
closed furnace or cooling chamber at a rate not greater
than 500°F/hr (280°C/h) divided by the maximum metal
thickness of the shell or head plate in inches, but in no case
more than 500°F/hr (280°C/h). From 800°F (425°C) the
vessel may be cooled in still air.
The second part of this analysis is to have a PWHT procedure that identifies which locations will be heated and thermocouple placements. Note, the entire weld and surrounding base material (the heat affected zone) must be subjected to PWHT time at temperature requirements mentioned above. Verification of PWHT time and temperature will be based on a chart recorder that should be used as part of a PWHT procedure.
Portable hardness testing is also specified by clients, as your mentioned, to ensure PWHT has softened the weld and surrounding base metal heat affected zone.
The above information should get you started.