I assume your gap is on the indoors side?
Regardless, if air is filtering through into the living space, there must be a gap outdoors ( external chimney) as well as indoors.
I recommend you check out the caulking along the chimney to the exterior siding as well as addressing the interior gap. Since this gap inside is directly adjacent to wood trim, I also have to assume that excessive heat is not a factor. Is the metal you are referring to an insert trim of some type? A pic would be a big help here.
If the assumption are right and the gap is 3/4 inch wide, I would use a caulking backer in the gap before using a good grade painter's or acrylic caulk as a topper. The caulking backer is a round foam solid tube that can be cut to length, inserted into the gap to seal it and hold the caulk. After the caulk has cured, it can be painted to match the trim. If for some reason you are concerned about high heat in this area, there is a fire rated caulk made especially for gaps in fire or common walls. Readily available at any box or hardware store from a number of manufactures.
Ok after reading your comments, and learning that the black vertical sides are slate, I would still do similar to above. Perhaps after injecting larger amounts of fire rated caulk as deep into void as possible, then use the solid, tube style caulking backer to fill the majority of the larger, deeper gaps, followed by using some paint-able silicon/acrylic mix caulk.
Before you apply the finish caulk, run a nice straight line of painter's tape up the front of the slate even with the edge of the wood trim. When you fill over the foam backer with the caulk, use a small putty knife to draw the caulk smooth and flat. Immediately remove the tape while caulk is fresh. This should result in a nice crisp straight line. Let the caulk cure for 24 hours. If there is some shrinking or cracks, no problem, simply repeat the process with new tape and another coat of caulk.
Alternately, you could also use a setting type drywall mud, such as durabond 30 or 45 to fill the deeper gaps etc. Then again use a second coat to create a smooth straight extension of the wood trim to the slate.
Either method will result in a neat, easy to paint fill that should stop your air infiltration problem and make the finish look nice.
If there is moisture still there, then mold and mildew will return. If the problem was not fixed, then it will return. Bathrooms are particularly bad in this respect, since moisture is a natural consequence of using water. I would expect to need to redo things like caulking every few years to fix this. It will not last forever.
Scrape/pull off the old silicon.
Apply a solution of bleach to kill the mold. Be careful when you apply it, as bleach can damage the clothes you are wearing. Keep the area ventilated well.
Let it dry. If you are in a hurry, a fan blowing on the area will help. A hair dryer can also speed that process considerably.
Apply new caulk in a smooth bead. I use my finger to spread it along the joint. Definitely use a high quality silicon caulk with a mold/mildew inhibitor. These are caulks that are designated for use in bathrooms.
Allow it to fully dry before you get it wet again. Give it a day or so. It will skin over in an hour or so, but make sure it has properly cured before use of the shower.
Expect to redo this process in some number of years. The exact time it will last depends on how well the area is ventilated.
Of course, there may be mold in the wall itself. This is difficult to deal with unless you tear the wall down to replace it completely, and even then water tends to attract the stuff. Mold spores are everywhere.
Best Answer
Furnace cement will work fine, you can also use, thinset, any setting type drywall mix, or High temp High density spun insulation. They all will work good as a caulk backer.