I would say that it's only a real fire risk depending on where the PC is in relation to other flammable materials, if its in an enclosed space & how hot your PC gets. There must be hundreds (or thousands) of servers across the country that are one 24/7 that are fine (OK some of them are in temperature controlled environments, but there are also ones that aren�t).
Not sure on how much electricity is used with the just the PC running. Is this of any use?
http://eetd.lbl.gov/EA/Reports/39466/39466-2