Make use of the flame carefully on the curled shingle edges.
Fix a leaking roof in winter.
Perhaps placing tube on furnace duct so air heats pre cut tube inside of home then climb up ladder and seal area keeping the sealant warm and easily caulk able.
Sealing the shingle to the object can be accomlished with a roofing sealant available at menards lowes etc.
How to repair a leaky roof from inside the house.
Identify the potential source of the leak.
The roof shingles should be softened and flattened as the shingles tend to curl up in winter.
Your best solution may be to just tarp off the problem area until the spring but be sure not to block off any venting pipes that vent out dangerous gasses.
Now is a time when you can start planning if you know where to start.
For example soak the downhill side of a chimney first then each side then the top on both sides.
Isolate areas when you run the hose.
If a leak is difficult to find enlist a helper and go up on the roof with a garden hose.
Recaulk the corner flashing if any areas have hardened caulk.
Replace any missing or rotted siding above the step flashing on dormers.
Locate the source of the leak by examining the underside of the roof from within your attic or crawl space.
In the winter a dab of roofing cement or tar should be added to each shingle to bond them together until the tar strip is activated in warmer weather.
Dig out any cracked or dry caulking that isn t properly sealing adjoining surfaces and replace with silicone caulk.
The shingles can be warmed up with a propane torch.
Locate the leaking source and search for the damaged or missing shingles and make a list of the areas to be repaired.
The secret to caulking in winter time is to heat the sealant in the tube.
The tar strip needs to be about 60f to activate.
Shingles that aren t stuck to one another are very susceptible to damage in winter winds.