Using extreme-ultraviolet images, we recently proposed a new and alternative formation mechanism for coronal rain along magnetically open field lines due to interchange magnetic reconnection. In this paper we report coronal rain at chromospheric and transition region temperatures originating from the coronal condensations facilitated by reconnection between open and closed coronal loops. For this, we employ the Interface Region Imaging Spectrograph (IRIS) and the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO). Around 2013 October 19, a coronal rain along curved paths was recorded by IRIS over the southeastern solar limb. Related to this, we found reconnection between a system of higher-lying open features and lower-lying closed loops that occurs repeatedly in AIA images. In this process, the higher-lying features form magnetic dips. In response, two sets of newly reconnected loops appear and retract away from the reconnection region. In the dips, seven events of cooling and condensation of coronal plasma repeatedly occur due to thermal instability over several days, from October 18 to 20. The condensations flow downward to the surface as coronal rain, with a mean interval between condensations of 6.6 hr. In the cases where IRIS data were available we found the condensations to cool all the way down to chromospheric temperatures. Based on our observations we suggest that some of the coronal rain events observed at chromospheric temperatures could be explained by the new and alternative scenario for the formation of coronal rain, where the condensation is facilitated by interchange reconnection.