(grrr, was typing out a response and my browser lost the window)
(take 2)
Heat (Btu/hr) and temperature (degrees F or C or whatever) are
NOT the same thing.
To heat up a tie rod, you need enough
heat.
Which can come from a combination of flame temperature and flame size.
Different torches, even with the same fuel and oxidizer, can produce different amounts of
heat output.
re: the little oxy-propane torch sets
Nope, not enough
heat from that little flame (although it certainly is hotter than an air-propane flame) to heat up a tie rod enough to do much good.
And those little 1.1 ft3 oxygen cylinders run about $10 each and only last about 20 minutes or so, depending on exactly how you set up the flame size.
http://www.bernzomatic.com/product/ox2550kc-cutting-welding-and-brazing-torch-kit/
http://www.bernzomatic.com/content/uploads/2015/05/WK5500OX_instructions.pdf
I have and have used this torch. It can heat up small things bright red hot, it can braze small things, and it can even oxy cut small steel items.
But the torch and flame size do not put out enough overall heat to get a tie rod hot enough.
It would be like trying to light up your living room with a laser pointer instead of a 60 watt light bulb.
Laser = focused and very intense light, but not a whole lot of overall light output (lumens)
plain old light bulb = enough light (lumens) to light up the room
Back to heating up you car parts.
You need a hot enough and big enough flame to get your steel parts hot enough.
Big daddy would be oxy-acetylene. With the 'right' size torch tip for the task at hand.
One step down would be an actual oxy-propane torch. Not the little Bernzomatic, but an actual welding/cutting/brazing torch from the likes of Victor, Harris, Smith or such.
A step down from there would be an air-acetylene torch.
A step down from there would be an air-propane torch with a big enough flame to get enough heat into your tie rod to do enough good.
A little pencil-flame air-propane plumbers torch doesn't produce enough heat (Btu/hr) for this task.
A bigger flame from a turbo/swirl air-propane torch might or might not be just enough heat output for you.
An air-propane weed burner can produce enough heat (on the order of 300k Btu/hr !!!) but is not all that controllable underneath a car.
An oxy-propane brazing/heating tip or a 'rosebud' oxy-propane torch tip might get the job done.
A big enough oxy-acetylene tip will get the job done.
Your call as to how you want to do it.
But as mentioned multiple times above, the current "MAP" gas (MAP/pro stuff, where the 'pro' is for propylene and not 'professional') is a propylene gas blend with about 10% more heat output than plain propane.
The old actual MAPP gas was about 25% more heat output than plain propane, if the torch burner head could utilize MAPP (some could, some couldn't). But since there is no more MAPP (not counting trying to find a garage sale cylinder here or there) available, it doesn't matter what MAPP used to be able to do.