Question

how will you sow experimentally that metals are good conductors of heat

Answer 1

take a knife and butter its sides well. take a candle and light it. hold just the tip of the candle over the flame. we will notice that the butter on all sides start to melt in a short time and drips down. thus we see that metals get heated up faster i.e. they are good conductors of heat

Answer 2

Generally the fact is, metals are good conductor of electricity as well as heat so if you prove that a substance is a good conductor of heat it may be good conductor of electricity as well, which can be showed easily, put a wooden spoon and a steel spoon in a cup filled with hot water and observe the end of spoon.

From similarity principal you can say that the spoon with higher temperature tip, is also a good conductor of electricity as well.

You can take the conductivity as well.

Hoping that will help.