The preface of the book "[ESSENCE OF VIRAT PARVA OF MAHA BHARATA][1]" states that it is believed that recitation of the Durga Stuti done by Yudhishthira just before entering the Virata Kingdom is capable of bringing even unseasonal rains.

> There is a strong belief that reading of Virat Parva of Maha Bharata
> would not only entail enrichment of one’s thought and action but
> toughen one’s psyche to face life in the framework of fortitude and
> challenge without slipping into demerit and immorality. **An allied
> faith is that daily recitation of ‘Durga Stuti’ -vide the sixth
> chapter of this Booklet- before Pandavas entered the Virat Kingdom-
> would usher in supreme faith and courage of conviction. In fact at the
> daily congregations of the five week long stay at the premises of Shri
> Lakshmi Kamakshi Nilaya mentioned above, HH Vijayendra Saraswati
> encouraged the open recitals of the Durga Stuti. Recital of this Stuti
> along with Rishyashringa Shlokas had indeed made it possible the
> typically Chennai weather of scortching heat to yield relieving but
> highly unseasonal rain pours as though Lord Indra Deva was happy at
> these daily recitals!**

The Stuti,which is included in the above PDF and  found from page 12 onwards,goes like this(for the full Stotram refer to the PDF or to the page linked below):

> Vaishampaayana narrated to King Janamejaya as follows: Virata nagaram
> ramyam gacchamaano Yudhishtharah, Astuvanmanasaa Deveem Durgaa
> tribhuvaneshwareem/ Yashodaa garbha sambhutaa Naraayana
> varapriyaamanda gopaala kuley jaataam mangalyaam kulavardhineem/
> Kamsavidraavana kareemasuraganaam kshayamkareem, shilaatata
> vinikshitaamaakaasham pratigaamineem/ Vaasudeva - sya bhagineem divya
> maalya vibhushitaam, Divyaambaradharaam Devim khadagakhetadhaarineem/
> (King Yudhishthar at the time of Pandavas entering ‘Virat Sabha’ had
> within his own heart prayed to Tribhuvaneshwari Durga Devi and further
> to Vaasudeva Shri Krishna the Avataara Purusha or the Singular Deity
> of Dwapara Yuga! Durga Devi’s ‘amsha’was also born to Nanda gopaala
> even as the babies were interchanged as Maya flew away to high skies
> warning Kamsa for having imprisoned his own sister and brother in law
> viz. Vasudeva and Devaki and that Lord Krishna would eventually
> terminate the devilish Kamsa) Dharma Raja further prayed to Durga
> Devi: Bhaaraava tarane punye ye smaranti Sadaashivam, Taan vai
> taarayase paapaat panke kaamiva durbalam/...

It is important to note,that neither the Phalasruti of this Stuti nor Durga Devi Herself specifically promised that recitation of the same will bring rains or that it has anything to do with rains.

One can read the Stuti on [this][2] page as well.

As one can see, the last verse of the Phalasruti simply states:

> There is nothing in this world that they cannot be got, By reading or
> hearing this great prayer with devotion, Due to my grace all the
> people of the city of Virata Would meet success in all their
> endeavors, Oh son of Pandu


  [1]: http://www.kamakoti.org/kamakoti/articles/ESSENCE%20OF%20VIRAT%20PARVA%20OF%20MAHA%20BHARATA.pdf
  [2]: http://www.hindupedia.com/en/Durga_Sthuthi_by_Yudhishtra