Adding Heat to Cool a Metal

That would make a nice air conditioner or refigeration unit wouldn't it?

Too bad physics says no.

and a very efficient, and green heat exchanger, I must add. GA, guest.

Surely you jest jasper! There are solid state electrical devices that become cooler as you add electrical energy to them, but that is not what you asked.

I am curious, what you were considering when you thought of this question. I can't imagine that you would have a misunderstanding of the basic concept of heat transfer. That is, after all, fundamental to the sense of touch so I must assume that your question was somehow misstated.

There are materials that will evaporate rapidly (thereby cooling) when heat is applied. Cooling towers perform this function but require replenishment to compensate for loss due to evaporation. Is this what you mean?

There is a possiblity, though may be in area of more of theoritical physics.

From the angle of latent heat -

The phase transformations - including solid-solid transformations have associated latent heats - though never went in details of these, Some metallurgists or Chemists may comment on this. Also whether these latent heats can cool ?

may be yes - like solid - liquid transformations (evaporations) do bring down the over all temperature of the system (water+vapour).

sb is right, that there are very narrow temperature ranges where the temperature does drop even while there is continued heat input but only until the phase transformation takes place. the reason is that during the phase transformation the material is generally expanding and becoming less dense much faster than the heat being added can compensate for. but this usually lasts for no more than a degree or so at melting and boiling points where the material is in a hybrid state between the two phases. if you were to graph the temp you'd have a linear line with small (very small) horizontal plateaus at the two phase changes.

If the metal starts out hotter than the heat being applied, it would get colder.

But, only until it reaches equilibrium with the applied heat.

In my knowledge - NO.

For the simple reason, the heat will travel to colder zones even, during phase changes. You may be able to cool the material if there is a still colder atmosphere available to reject the transported heat.

The properties of such a material would take it outside the laws of thermodynamics. What is the application, an over-unity energy device?

Ummm...no.

However, I would like to state for the record that in my humble opinion that would truly be a "cool" metal to discover! ;)

I think the part of your musings that got you into trouble was the words "cooler" and "heat." Think of it instead as asking;

"Is there any metal or element that as the molecules are energized by an outside source (of energy), they instead "slow down" to a lower energy state."

It will sound a tad like an over-unity question when posed as "is there any thing that speeds up as you slow it down" or "how do I build a machine that increases in system energy as I remove energy?"