Why is very important to wait until the crucible is fully coleed to room temperature before weighting

If you do not wait until the crucible is at room temperature, its density will vary constantly until it reaches this temperature, since density is a property that varies with temperature. For the above reason, weighing a hot crucible will not allow the measurement of a constant weight on the balance, since the weight of the object will be constantly changing, which will not allow a constant reading.