ASME has a different philosophy than AWS. AWS codes take a cookbook approach to welding. They assume the user has a basic knowledge of welding, but not at the expert level. If one follows the guideline successful results should be achieved.

ASME takes the approach the user is an expert and knows what to do. ASME requires the user to qualify the WPS to demonstrate successful results can be achieved. In short, do not look to ASME for any more than minimal guidance.

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These steels are frequently used for ASME B31.1 and ASME B31.3, both will have some minimum requirements on what the preheat and pwht temperatures should be for different thicknesses.

If you are welding under these codes, just check the respective tables, but if not, you can use them as guidelines.