If there is a DC voltage across the collector-emitter then a small current will flow through the finite off resistance of the transistor. However, this through the collector. Another option, is to have an AC voltage and say there is power loss due to the small current flowing through the parasitic capacitance of the transistor.
I think the answer is that there is power dissipation due to the random motion of electrons in the transistor and vibration of the atoms of the semiconducting materials and this dissipation depends on the ambient temperature.
In a perfect world, I would have to agree; that is, no power dissipated if no voltage source is applied on the transistor . However, there is a thing known as nanoscopic leakages in the materials utilized to make such devices. Hence, too broad of a question to advice.......