The balance in calibrated to work at a specific temperature, if the object being weighed transfers heat into the balance pan it will heat things up. Metal expands and contracts with different temperature, even a slight temperature change can cause enough change in distance of the internal components to give bad readings.
Another is the air. The heat will transfer to the air. If the balance is in a enclosures (which it should be to remove any variations do to air current), when the temperature of the air increases the pressure inside the closed container will increase; pushing down more on the balance pan throwing off the reading.