Do not heat the rail by shunting a 12v power source (like a big battery) through it. You get what is technically known as "a fuse".
I've tried the heat and suspend method. It sort of worked but it was difficult to get a consistent temperature.
There is a technique similar to the "draw through finger & thumb" method which can get a lot of the curve out, both vertical and horizontial.
Obtain a block of 18mm MDF, size isn't critical but it needs to be weighty enough not to slip on the bench. Next, find a reasonably hard pencil eraser. Some are far too hard to erase nicely, these are ideal! With some suitable pliers (I use the Maun parallel jaw type), grip the one end of the rail. Using the eraser, press quite hard down on the rail flat-wise against the MDF and slowly draw it between the MDF and eraser, simultaneously pulling and curving the rail in the opposite direction to the prevailing curvature of the rail. I work on about 9 to 12 inches of rail at a time.
Hopefully this photo shows the basic technique
With a bit of practice, you can get the rail quite straight, certainly good enough to work well with soldered construction.
Then congratulate yourself at saving $85.
Mark