A polar molecule has one negative and one positive ending speaking in terms of electric charge. Because of this, in a liquid, positive endings of molecules attracts the negative endings of other molecules, forming what is called a dipole-dipole interaction. This interaction makes forces between polar molecules in liquids to be stronger than those between non polar molecules of other liquid, if the the size of molecules in both liquids is about the same. The name of these forces that arise from dipole-dipole interactions is Van der Waals forces. Thus to form a gas, more energy will be needed to be added to a polar liquid (the extra energy is necessary to overcome the dipole-dipole interactions and the corresponding Van der Waals forces) and the liquid will boil at a higher temperature.
Therefore substance A which boils at a higher temperature is more likely to have a polar molecule.