Engine fan stay on

I have had this car one week and so far fine. I drove to work this morning (6 miles)and when I took key out I could hear the fan running which it hasn't before and I am sure I smelled burning. Tonight on way home I stopped it in town and it was ok but when I went the last mile home it came on again. The coolant level looks fine. Iwent another run later where there is a bit of a climb but it was ok. Should the fan be coming on on short journeys?