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?