The rate of ice-cream melting is proportional to the rate at which heat flows from the outside INTO the ice cup.

Hence if the ice cream was in a thin walled metal cup, it would melt faster than if the ice-cream was in a thick paper or Styrofoam cup. This is because metal has a higher thermal conductivity (heat flow faster) than a plastic cup of the same thickness.

There are two main factors that go into a "type" of a container that affect the exchange of heat through the container. One factor is the material that the container is made of. We can classify materials as thermally insulating or thermally conductive.

A thermal insulator is something like plastic or wood. Neither of these materials heat up very fast, but they also don't cool down very fast. Heat has a hard time moving through these materials. A thermal conductor would be something like metal or glass. Both of these materials heat up well (which is one reason why pots and pans are glass or metal!), and they can cool off or heat up relatively quickly.

So, if we have ice cream in a plastic bowl, it would probably melt slower than if it were in a glass bowl of the same size. The glass bowl could conduct the heat from the environment to the ice cream much better than the plastic bowl, so the ice cream would melt faster.

Another factor to consider is the dimensions of the container that the ice cream is in. To visualize this, let's think about two metal rods, one five feet long and one two feet long. I stick one end of each rod into an oven and let them sit for five minutes. If I touch both the ends of the rods that are sticking out of the oven, which one will be hotter? The short rod will feel hotter than the long rod, because the heat from the oven has to travel farther for the long rod than the short rod.

Objects that are thinner or shorter will heat up faster than objects that are thick or long, because the heat has to move through more material.

Back to the ice cream--if you scoop some ice cream into a glass jar and some into a glass wine glass, which will melt faster? The jar and the wine glass have similar dimensions, but the wine glass is thinner than the jar, so probably the ice cream in the wine glass will melt faster.

In practical terms, your ice cream is probably either in the container you bought it in or the bowl you eat it from. Based on my experience, it seems like the ice cream melts faster in the container than in the bowl. Can you think of an explanation for this? What is it about the material, size, and shape of both materials that accounts for the different melting times?

The more the container absorbs heat, the more rapidly the ice cream will melt. The melting rate depends on the temperature.

Ice cream melts at 32 F. Room temperature is about 77 F. To stay a solid, it must be kept at a lower temperature than 32 F. This is why we keep ice cream in the freezer at 0 F. So, no matter what container, the ice cream should not melt in the freezer.

When you take it out of the freezer, it takes some time for the ice cream to change temperatures from 0 F to above 32 F. Heat from the surroundings must transfer to the ice cream. Now, if you have a container that keeps heat from going to the ice cream, then you can slow down the temperature change, keeping your ice cream from melting for longer. The thermal conductivity of a material affects how fast heat passes through the container and into the ice cream: a higher thermal conductivity means heat passes through the material faster. In the following website, you can see values for different materials---a lower thermal conductivity means it's a good choice for holding your ice cream (as long as the material is safe to hold food of course).

thermal conductivity for different materials

A few basics on melting before we attack your question in total. Broadly speaking, melting is a process in which heat transfers between objects and their surroundings, and in this scenario, heat entering the ice cream will cause it to melt into a liquid. Therefore, any way in which heat can more efficiently enter the ice cream, the quicker the melting process will occur.

Now, to a more practical concern of how to keep the McConnell’s Turkish Coffee Ice Cream from melting. Firstly, containers not to use in respective order of material, size, and exposure of the ice cream surface (non-exhaustive): metal (this will conduct the heat from the environment very effectively into the ice cream); small containers (this will leave very little of the ice cream protected from heat entering it); and finally, a large area of the ice cream exposed to the environment (this will allow more opportunities for heat to work its way into the ice cream). Secondly, containers to consider using in respective order of material, size, and exposure of the ice cream surface (non-exhaustive): plastic (this will not conduct the heat from the environment very effectively into the ice cream); larger containers (this will leave more of the ice cream protected from heat entering it); and finally, a small area of the ice cream, if any at all, exposed to the environment (this will allow fewer opportunities for heat to work its way into the ice cream).