If the melting point of the compound is unknown the melting point measurement could take an exceedingly long time if the rate of heating of 2C/min is followed over the entire range from the room temperature to the  melting point . What technique can be used to make this more efficient?

To determine the melting point of the unknown substance if approximate melting point is not known, it is better to make or fill two capillaries with the same substance. The temp of the heating liquid bath may then be raised fairly rapidly using one capillary tube in order to determine the melting point approximately, the bath is then allowed to cool about 30deg C and second capillary tube is substituted for the first and accurate determination is made .It should be noted that a second determination of melting should not be made as the bath liquid cools by observing temperature at which the molten material in the capillary tube solidifies. This is because in many cases the substance may partially decomposed or some changes in its crystalline form which may change its melting point.

Uma your mind is like a carnot engine of 100% efficiency that defies thermodynamics law.

Hey Manju Thanks for your appreciation .But dear we can not break natural laws and I am not an exception.