My comment was taken out of context! Truth is, I always carry aspirin for these situations. "How about it?" "I have a headache!" "I have an aspirin!"
lets use a margin value as to make clear what I said: imagine a material with an infinite heat conductivity. you put it in the fridge, it's instantly the same temperature as in the fridge. you take it out the fridge, it's instantly the room temperature, and by the time you put it against your forehead, you could aswell slap your head for no reason. abit away from this margin value: you only have a minute of 'cold'. abit further away: you have 2 minutes. This makes clear that a higher heat conductivity doesn't make it better / more efficient as a 'cold pack'. Like alot applications, it's a trade off, and using silver instead of water in a cold pack just inflicts you more trips to the fridge, as a net result pro/cons. For the same reason, it's exactly the opposite as your last sentence, see the margin case example: with an infinite heat conductivity, it's completely useless to have a second bar in the fridge. Put the first ('used') one in the fridge, and it's instantly cold. Why then having a second?
The high heat conductivity does indeed make the bar better and is not negated by being in contact with the air due to air being about 1000 times less dense than your skin. So hardly any heat diffuses into the bar from the air compared to how much diffuses into the bar directly from your blood flowing past the bar at your temples or forehead. It is simple to empirically confirm this. For the same reason it is quicker to cool a 1kg bar down by melting a small ice cube on it for 30 seconds which gets it as cold as you'd want it, rather than putting it in the fridge where again, it is being cooled by the much less efficient air contact.
I reckon if you dropped one of those bad boys on your foot you'd forget about your headache in a hurry.
