Storing alpha values in temporary RenderTexture

I've written an edge detection image effect, and I want to apply additional effects such as blur (only to the edges) before I blit them to the camera's destination RenderTexture, but I've run into some problems.

In the shader, I set the alpha of all non-edge fragments to 0. This way, I can get the edges in their own texture and I can do what i want with them. If I blit the effect as in the following code, I get the original image + edge detection, as expected:

Code (CSharp):

1. void OnRenderImage(RenderTexture src, RenderTexture dst)
2. {
3.         Graphics.Blit(src, dst);
4.         Graphics.Blit(src, dst, _edgeDetectionMat);
5. }

If I only do the second blit (using _edgeDetectionMat), I only get edge detection - everything else in the image is black, also as expected.

However, I still want to separate the edge detection into its own RenderTexture. So I tried the following:

Code (CSharp):

1. void OnRenderImage(RenderTexture src, RenderTexture dst)
2. {
3.        RenderTexture tmp = RenderTexture.GetTemporary(src.width, src.height);
4.  
5.        Graphics.Blit(src, dst);
6.        Graphics.Blit(src, tmp, _edgeDetectionMat);
7.        Graphics.Blit(tmp, dst);
8.  
9.        tmp.Release();
10. }

Here, I expect to achieve the same result as in the first block of code, where I get the original image + edge detection. But the image only shows the edge detection and everything else is black. Maybe I lose all alpha data once I make the temporary RenderTexture?