Water is a poor conductor

In the three states of matter, in general, solid is the best conductor as the particles are closely packed in an orderly manner, hence thermal energy can be passed down by the collision of the particles in the solid faster.

On the other hand, liquid and gas are relatively considered poor conductor. Gas is the worst conductor as the particles are far apart.

The following experiment demonstrates that water is indeed a poor conductor of thermal energy.

An ice cube is kept at the bottom of the boiling tube by the net. The water at the top of the boiling tube is heated and started to boil. But the ice is not fully melted.

This shows that thermal energy transferred through the water from heated water at the top to the ice is weak, hence indicating that water is a poor conductor.

How about thermal transfer through convection current? In this experiment, the heated water at the top expands, the volume of the heated water increases, becomes less dense and remains at the top. The cooler water, which is denser, remains at the bottom. Hence there is no convection current formed throughout the entire water in the tube. So thermal energy transfer to the ice cube through convection is not present here.