I would clean the logs as soon as possible. If the mold is allowed to sit on the logs for any length of time it will start breaking down the finish. You should wash it with 4-5 gallons of warm water mixed with 1/4 cup Dawn liquid dish soap and 1/4 cup of chlorinated bleach to kill the mold spores. You should use a latex caulk that is made for log homes. Energy Seal is a very good choice. You can get it from Timeless wood Care Products at 800-564-2987 or timelesswoodcare.com.