How to pass Mesh type by value

I have the following code:

Mesh thisMesh = GetComponent<MeshFilter>().mesh;
Mesh tempMesh = thisMesh;

It appears that assigning a mesh is done by reference, since if I make any edits to tempMesh, thisMesh will be affected as well.

Is it possible to assign a mesh by value, so that I can edit tempMesh without affecting thisMesh?

No; you can instantiate a new mesh.