Which pipe code?

Some of the pipe codes do not allow any oxy fuel heating - even for pre-heat.  Off hand I would say you would need customer approval even if the code allows it.  Check the code first.

Flame straightening can be used if certain precautions are observed to minimize the chance of violating code requirements or causing metallurgical issues that may be considered damaging to the pipe.

First point: you do not need to heat the base metal, in your case I assume it is carbon steel, over 600 to 800 degrees F to get the pipe to "move" by introducing residual stress that counter the existing residual stresses from the welding operations. The temperatures noted above are well below the temperatures where phase transformations begin, i.e., transformation from pearlite and ferrite to austenite, so there is no danger of increasing the hardness of the base metal due to rapid cooling from the austenizing temperature ranges.

Second point: the area where you apply the heat is going to cause the distortion to become more pronounced than it already is. However, upon cooling the area initially heated will contract and "pull" in the opposite direction. Upon cooling the residual stress is in tension. So, if the pipe is distorted toward the right of this page as you read, you would heat an area on the left side of this page. The added heat will cause the pipe to deflect toward the right initially, but upon cooling it will pull the pipe back toward the left past th starting point.

Third point: do not heat the entire pipe diameter. Apply the heat in pie sections on the side that you want the pipe to pull in. The pie section should extend to the center line of the pipe. You can pack wet rags adjacent to the area being heated to limit the transfer of heat to the areas not heated. This technique depends on a high temperature diferential between the area heated and the adjacent areas not heated.

Use temperature indicating crayons (Tempil Sticks) to monitor and control the temperature. There is no need to heat the pipe to temperatures higher than 800 degrees F. Heat the pie sections to the temperature indicated and allow it to cool to ambient temperature to assess the amount of movement you get. You can repeat the process to either side of the initial area heated if more movement is required.

This can be a slow procss until you learn the tehnique with a couple of tries to see how the pipe moves.

Best of luck - Al