Fan Doesn't Stop After Furnace Shuts Off

I have a new furnace that worked fine for 3 months. Now I have two problems: 1) The fan continues to run & blow cool air after the furnace shuts down (randomly). Sometimes I have to manually turn the heat off to stop it. Other times it will stop after 5 minutes or more. 2) The house temperature sometimes drops below the thermostat setting. One evening the thermostat was set to 65 but by morning, the house temperature was 60. Once I turned the furnace off & then back on, it was fine. Any ideas?