Actually, dry ice DOES indeed melt:
Dry ice (solid carbon dioxide) DOES melt like regular ice. The difference is that the pressure of the vapor of dry ice at its melting point is about 5 atmospheres. This occurs at a temperature of -57 C. Now when you have a lump of dry ice in a container of some sort, the pressure applied by the atmosphere on the dry ice is only 1 atmosphere, rather than 5 atmospheres. The temperature at which the vapor of dry ice is 1 atmosphere is -78 C, which is lower than its melting point. So the dry ice passes directly from solid to vapor because you don't have the needed 5 atmospheres for it to form a "normal" melting liquid.
This is not all that mysterious. It happens with water all the time in the winter where often we can observe frost disappearing from a window or driveway in the morning without first melting. The process is a little different, but the concept is the same. In the case of frost, the wind blows water vapor away at temperatures less than 0 C., and eventually all the frost (ice) disappears without ever turning into a liquid.
Vince Calder
It is still the best choice for long term in an ice chest.
Dale