My compost bin is not heating up, should I move it into the sun?

No, the bin does not heat up because of the sun, the heat is produced by the action of bugs, bacteria and fungi decomposing the waste, they need to have a good supply of air to work, if your compost is compacted, give it a good stir, if its wet add in some shredded paper and/or cardboard, this should kick start it into working.