If you are going to be home alone, then make it into a cosy xmas just for you. Pick out all the tv you are going to watch, get yourself something really nice to munch on.. whatever your favourite comfort food is.. or just pig out on chocs all day!
Sort your heating so that it is only on in the living room (turn off all other radiators, you dont need them on).
Either that or be really brazen with your hints and get your status on facebook (if you have it) as
"anyone got a bit of turkey going spare on xmas day"
I know if I saw that one of my friends was going to be on her own, I wouldnt hesitate to invite her over to my house for the day.