Please help a family dispute. What is the optimal temperature to keep the furnace at during the day and night during the winter months, and can keeping the temperature too high result in increased illness?
For the most part, at what temperature you set your thermostat is a matter of opinion. Unfortunately for you, it sounds like there are too many opinions and no consensus. Worth mentioning, there is research to support that it is better to lower the heat before you go to bed at night. Cooler rooms with well-circulated air are more conducive to getting a good night's sleep. If the house is too hot, it's not the heat per se that will promote illness, but the dryness created by most heating systems. When people are trying to get over winter colds, it's common for health care providers to suggest cracking open a bedroom window or using a humidifier at night. If illness is your greatest concern (and you can't agree on anything else), perhaps your family can work together to create an environment to support quality sleep and health.
As for the daytime temperature, this decision could be left up to those people who are home during the day. Of course, if no one is at home, it's best to turn the heat down low to conserve energy and save money on your heating bills. But, if more than one opinionated person is home all day, perhaps they can alternate between warm and cool days. The people who prefer higher temperatures can wear thermals and sweaters on designated "cool days." Likewise, the warm-blooded members of the household can wear shorts and t-shirts on "warm days." Or, you can keep the temperature low and invest in space heaters for the thin-skinned people among you. Or, if you none of these suggestions are appealing, your family can brainstorm together to come up with a few other solutions to the problem.
Your family may never find a setting on the thermostat that everyone is comfortable with because we all tend to have different tolerance levels for heat and cold. From your question, it seems your family is no exception. Hopefully you'll find a way to accommodate everyone's needs (at least part of the time). Unless you would prefer to fight about it all winter, until summer, when you can then argue about the air conditioning.