The answer to this question is yes and no.
No It Doesn’t!
When most people wonder if dry ice melts, they are referring to your normal everyday use of dry ice. In this case, no, dry ice does not melt. Dry ice in normal earth atmosphere sublimates. Sublimation is the process of turning directly from a solid to a gas. In other words, dry ice turns from the very cold block of ice in to CO2 gas. This is very different from what most people are used to with regular ice created from water, which goes from solid to liquid to gas. This is one huge advantage to cooling perishables with dry ice… no messy liquid cleanup!
Yes It Does!
To really answer YES to this question, you will need to understand a little bit about how dry ice and liquid carbon dioxide are made. Dry ice is solid carbon dioxide. The dry ice is actually made from liquid CO2 after it has been depressurized. To create liquid CO2, pure carbon dioxide must be compressed and cooled. The liquid carbon dioxide is then depressurized and bingo, dry ice. You can see the full article here. What this tells us is that liquid carbon dioxide can only exist in a highly pressurized atmosphere with very specific temperatures. The carbon dioxide gas must be pressurized to 5.1 atmospheres and cooled to -56.6 C to produce liquid carbon dioxide.
To get back to our question, the way that you get dry ice to melt is just the way that you made it. You need to pressurize the dry ice and get it back to the correct temperature. Pressure and temperature are key to creating the liquid CO2. If you get those right, your dry ice should turn back in to a liquid.