What common metals conduct heat the best?

Thermal conductivity is highest in Silver, followed by Copper, Gold, and Aluminum.

Cost is a factor in all things so in practice you will find copper and aluminum used in a lot of applications for industrial and household use. Decent performance at an attractive price.

You have stainless clad copper or aluminum for pots and pans in your kitchen…

Stainless is a relatively poor conductor, but a thin layer minimizes its effect when the core distributes the heat really well.

Aluminum is often used to conduct heat to provide cooling for electronics from computers of all sizes to your mobile device.

Gold and silver are sometimes used for special applications and a combination of their properties. For example, gold not only conducts both heat and electricity really well; it is also highly reflective.  In fact it is used as the reflective mirrors on the James Webb space telescope.

Alloying elements negatively affect the thermal conductivity, so any alloys have to be evaluated when thermal conductivity is an important factor. Don’t forget to check the specs! For more on electrical conductivity check out this longer video.