It is exactly "mid-afternoon", and more precisely, it is three o"clock in the afternoon. The Trinitarian reference is used again, as always throughout his entire journey, almost over-emphasizing that special, divine number, three. The translator, Mark Musa, in his notes on lines 1-6, exposes the significance of the time and the number three. He explains that since Dante tells us it is 3:00 in the afternoon "up there" in Purgatory, and that it is simultaneously "midnight here" in the present time, the result is that "it is three hours before sunset in Purgatory" (Purg. XV, Notes 1-6). Furthermore, Dante-the-Poet is showing the reader the idea of the "mirror image" of the evening time in Purgatory contrasted with the morning time of the present moment (Purg. XV, Notes 1-6). And as Musa correctly determines, Dante is using ". . . the imagery of "reflection," which will dominate this canto" (Purg. XV, Notes 1-6).
Significantly, Canto XV is about the halfway point through Purgatory, so Dante is halfway to reaching the sunset of his journey to Paradise. Furthermore, just like knowing that one is in the middle of a journey, there is a pressing desire to continue for one has only to duplicate the distance already traveled to reach one's destination. Since after a halfway point is reached, the distance remaining to the end is always less than the distance already traveled. "The same amount of time it takes that sphere (which, like a child at play, is never still) to go from break of day to the third hour, was left now for the sun to run its course toward night" (Purg. XV, 1-5). It is possible that this is the sort of feeling Dante-the-Poet wants the reader to have from the start of the Canto because of the way in which he personifies the "spera". If the movement of the sun is supposed to connect to Dante's own journey through Purgatory, then Dante (and through him the reader as well) is symbolized by the sun.
