Like tomatoes, fresh tamarillos should be stored at room temperature until they are fully ripe, which may take several days. Once they are ripe, you can store them in the refrigerator for up to a week. If you have a large quantity of tamarillos, and want to store them for a longer period of time, you can freeze them. To freeze tamarillos, peel and remove the seeds, then cut them into quarters or slices, and place them in a freezer-safe container or bag. Frozen tamarillos can be stored for up to 8 months. Whe you are ready to use them, thaw the tamarillos in the refrigerator or use them directly from the freezer in recipes that call for cooked or blended fruit. You can also buy whole frozen tamarillos and tamarillo pulp in many Latin markets.