First, for your After Effects issue, directly from the AE 5.5 docs, (mildly edited), here is why it remains centered, and does NOT work with animated layers, but DOES work with frame sequences:

First tho, for best results, I personally use the Compound blur effect in combination with displacement

Anyhoo... from the docs...
"COMPOUND BLUR & DISPLACEMENT EFFECTS
These effects blur or displace pixels in the selected layer based on the luminance values of another layer (sequence), also known as a blur or displacement map.
The blur/displacement layer, which can be any layer that contains pixels of different luminance values, is essentially overlaid on top of the selected layer and the pixels of both layers are matched, one to one. Where the blur/displacement layer is black, no blurring/displacement occurs in the same location in the selected layer. The blur/displacement layer is used only as a map; it is not visible in the composition.

The blur/displacement layer sequence specifies the layer in the composition to use as the blurring/displacement map.
Bright values in the blur/displacement layer correspond to more blurring/displacement of the affected layer, while dark values correspond to less blurring/displacement.
Maximum blur/displacement specifies the maximum amount, in pixels, that any part of the affected layer can be blurred.

The Stretch Map to Fit option stretches the blur/displacement layer to the dimensions of the layer to which it is applied; otherwise, IT IS CENTERED
Invert Blur inverts the values, so areas that were previously more blurred will be less blurred, and vice versa.

This effect is useful for simulating smudges and fingerprints, or changes in visibility due to atmospheric conditions such as smoke or HEAT, especially with animated blur/displacement layer sequences.
Compound Blur is especially effective in combination with other effects, such as Displacement Map. (Production Bundle only)."


And here is a correction to my mistake (thanks for noticing Dave!) in my past post regarding ONE heat haze technique in Maya:

I just tried it, and you're right, do NOT try to re-connect a lambert to a particle SW cloud because when you create one, it already comes connected to the default CLOUD shading group.

I've included a Maya 4.5 .mb scene file for you to see what I did to get it working.
Check out every possible thing, so as to give you some ideas to better create your own effect

Basically, I did the following:

1. Create a basic OMNI emitter.
This creates a particle emitter and a particle object already connected to the default CLOUD shading group.

2. I tweaked the emitter to get it to "act" more like exhaust.
(a little bit)

3. I created a radiusPP attribute for the particle object, then right-clicked on the arrayMapper to create the default RAMP.
Then I edited the ramp and reversed the black and white colors so the particles would start out small, and end up big.
This step is optional, as the look is ultimately up to the artist.

4. Then, in the hypershade, I edited the particle CLOUD shading group a bit by turning the noise off, and cranking the transparency back down so that it would NOT be transparent. Again, this is optional, but my idea is that they will simply render out as simple opaque "disk"-shaped particles so you have more control over them in your compositing app.

That's pretty much it besides placing the emitter in the same place as your separate exhaust smoke emitter.

Just remember to render the smoke, and these "disks/clouds" out separately

Good luck all!