If you have an integrated heating, ventilation and air conditioning (A/C) system that uses the same distribution channel for all functions (e.g. central forced air), now is the time to make sure your ductwork and filtration are in good working order. Running your A/C during the summer can cause moisture to build up in or around the unit, which could allow irritating mould to grow and then circulate throughout your home when your fan is turned on. So check both your heating and your A/C for signs of mould.
Also, where possible, check for air leaks in the ductwork, particularly in bends and connections, as leaks could allow moisture to enter or collect in the system, and therefore give mould a chance to grow. Next, be sure to install clean HEPA (high-efficiency particulate air) filters to help catch undesirable air contaminants.
Finally, if you think you have mould growing in your heating and air distribution network, get a professional to examine and/or clean your system before starting your furnace fan.