Plants respond to stress through metabolic and morphological changes that increase their ability to survive and grow. To this end, several transcription factor families are responsible for transmitting the signals that are required for these changes. Here, we studied the transcription factor superfamily AP2/ERF, particularly, RAP2.4 from Carica papaya cv. Maradol. We isolated four genes (CpRap2.4a, CpRAap2.4b, CpRap2.1 and CpRap2.10), and an in silico analysis showed that the four genes encode proteins that contain a conserved APETALA2 (AP2) domain located within group I and II transcription factors of the AP2/ERF superfamily. Semiquantitative PCR experiments indicated that each CpRap2 gene is differentially expressed under stress conditions, such as extreme temperatures. Moreover, genetic transformants of tobacco plants overexpressing CpRap2.4a and CpRap2.4b genes show a high level of tolerance to cold and heat stress compared to non-transformed plants. Confocal microscopy analysis of tobacco transgenic plants showed that CpRAP2.4a and CpRAP2.4b proteins were mainly localized to the nuclei of cells from the leaves and roots and also in the sieve elements. Moreover, the movement of CpRap2.4a RNA in tobacco grafting was analyzed. Our results indicate that CpRap2.4a and CpRap2.4b RNA in the papaya tree have a functional role in the response to stress conditions such as exposure to extreme temperatures via direct translation outside the parental RNA cell.