Ok ... let's figure this out together. Here is my settings in PP11.2

Mat room settings and a raytrace preview to show what I want to "fix".

Here is my Render settings:

Now ... my challenge is how to soften the edges so I lose the hard edges of the prop and only see the fire? The interior of the obj is fantastic ... the edges Not so much. Note: the "fire" is the ONLY light in the scene.

The first thing, I see that might be an issue, is the transparency may bot be set up properly. Rather than the trans map going to the transparency color, usually the map is plugged into the fac of the mix closure and the transparency is set to white. To get a soft edge, you can add an edge blend with black on top and white on bottom. The amount of blurring of the edges is controlled by the attenuation. However, if you also want the transparency map you have in the scene, plugging that into the edge blend doesn't work.

okay, I plugged a mix node (in colors not the mix closure) into the white of the edge blend and set the top color to 1 and plugged the map into the bottom and blend type to add. that seems to incorporate both.

However, the setup doesn't seem to effect the volume. It renders the same with and without it.

This is only a suggestion, but maybe using the Physical Surface root node instead of Cycles might give you more control, especially with transparency.

These are great suggestions. I'll try these out. Thank you.

Latest results (the right render wasn't left to full rendertime so that's why it's a bit grainy)