I did the heater core replacement job on my 85 T-Bird which is darn close to the 86. It was a cold Janurary in New York. I did it nights in my unheated garage after work. It was probably 1992 or 1993. The real Ford Shop Manual helps alot. You have alot of good suggestions before my entry here. My two cents follows.
Keep track of what nuts and bolts and sheet metal screws go where.
Use the best quality replacement heater core you can get your hands on. You don't want to do this job twice.
Once you take care of the A/C issues you want to disconnect the battery.
Your car is not new. You are going pretty deep into the electronics and heating ductwork. You are not on the clock being paid by the hour. Look for other potential troubles to fix while you are down there this deep like cracked vacuum hoses, falling apart foam seals on ductwork, rusty control cables, worn insulation on electrical wires, maybe even water leaks.
Pull the instrument cluster and replace the halogen lamps used for cluster illumination and the instrument panel voltage regulator that is tacked onto the back of the cluster.
Be careful putting it all back together. Easy to pinch a wire, hose. or something else that will be a pain to figure out.