Unless the flu pipe is double-walled, it will probably get hot enough to melt the plastic and the duct tape. Sparks should be less of a concern with the cap and mesh.

Is there a woodstove dealer nearby? You might be able to squeeze some stove cement into the leak around the pipe (from the outside) as a temporary repair.

Failing that, I'd be tempted to try to make a temporary flashing for where the flu pipe comes through the roof, even if out of HD foil, and secure it with metal muffler repair tape, still available at most auto-parts stores.

Final option: use the plastic and duct tape, but accept the fact that the stove has to stay cold until the permanent repair is done.

And, seriously: good luck.

Frank2135