I completely agree it's poorly written and the forms of heat-treating it communicates are unnecessary for forming. In the rare even that a customer interprets this as it's written, we will take "exception" to it.
The word "maintain", in this section of API 934C, means you don't let the item being worked drop below it's preheat temperature until it can be DHT'd or PWHT'd. I've been involved in the fabrication of HEs and PVs that had API 934A or C applied. They are quite challenging.