As per ASME code, for pressure vessels and piping, if the thickness of the parts being welded exceeds a specified value, PWHT cannot be avoided. Charpy test properties of the material and the minimum service temperature required should determine this. In general, US codes limit the thickness of C / C-Mn Steels to 32 mm, beyond which PWHT cannot be avoided whether it be pressure vessel, piping or storage tank.
As per ASME code VIII Div.1 UCS-79 as it stated that the required material will need heat treatment when the resulting fiber elongation is more than 5% from the as rolled condition.
When comes to the low alloy steels, ASME B31.3 has set a limit thickness of 19 mm, above which PWHT cannot be avoided.
Refer ASME Section VIII - Div. 1, UCS-56 for Post Weld Heat Treatment requirements detailed. Also refer UCS-68 where it is mentioned that PWHT cannot be avoided when minimum design metal temperature is colder than -12 degree C.