I would venture that the final heart is most likely to be drawn in either 49th, 50th, 51st, or 52nd position (each occurring with equal probability).
In an infinite serious of trials, probability will ensure that after 12 hearts are drawn, 12 of each of the remaining suites (clubs, spades, diamonds) are drawn as well. This gives us 48 cards out and 4 remaining. It is not possible to determine whether or not the case heart will necessarily be drawn in the next card but at this point there is a 25% chance that it will be drawn in 49th, 25% for 50th, 25% for 51st, and 25% for 52nd.
Without hard math, common sense would suggest that the final heart will most often be found in this 4-card grouping (remaining 4) when compared with similiar groupings occurring before 48 cards are selected.