The Mishna Berura writes that the Shaliach Tzibbur dons a Tallit when the Thirteen Attributes of Mercy are recited, even if it is before sunrise, but does not say a blessing. The Levush explains that this is because of the doubt as to whether there is a clear obligation to say the blessing, since it is still night-time and the Tallit is considered a daytime garment. The proposed solution is that to borrow a Tallit with the intention that it is only in honor of the recital and not an acquisition. The Shevach HaMoadim writes similarly.
