There are a number of products available in the marketplace that advertise as fillers for checks, cracks, joints, windows, log ends and other areas in need of being sealed. However, it's very important that you only use products specifically designed for logs. Like your stain and finish, you get what you pay for with these products.
Caulking is commonly used on the top of any logs that have a check (a splitting crack in the log) over 1/8" to 1/4". If left exposed, these areas become moisture traps for water to run into and hide inside your log. Moisture is one of the primary enemies of logs because it leads to mold, mildew, and rot. During cold winter months this moisture freezes. During warm months the water will thaw then evaporate out. This movement within the log is usually what causes the checking in the first place, but will also cause existing checks to get larger, exacerbating the problem. Our goal is to minimize the amount of water getting into the logs.
Another important use of log caulks and sealants is to seal up the joint where logs meet walls and windows to eliminate drafting and increase energy conservation. These are often the same areas where flies, ants, and other bugs find their way into your home. They must be sealed!
Caulking application should be done by a professional who knows the appropriate application rates of the material. Applying too much or too little product will result in its failure. You should also be sure that a backer of some sort is used to ensure 2 point adhesion. This allows the caulk to move and stretch with the logs, preventing the material from tearing.