The laser-induced blackbody-assisted rotational cooling of a linear polyatomic ion, C2H2(+), in its (2)Π ground electronic state in the presence of the blackbody radiation field at 300 K and 77 K is investigated theoretically using a rate-equations model. Although pure rotational transitions are forbidden in this non-polar species, the ν5 cis-bending mode is infrared active and the (1-0) band of this mode strongly overlaps the 300 K blackbody spectrum. Hence the lifetimes of state-selected rotational levels are found to be short compared to the typical timescale of ion trapping experiments. The ν5 (1-0) transition is split by the Renner-Teller coupling of vibrational and electronic angular momentum, and by the spin-orbit coupling, into six principal components and these effects are included in the calculations. In this paper, a rotational-cooling scheme is proposed that involves simultaneous pumping of a set of closely spaced Q-branch transitions on the (2)Δ5/2 - (2)Π3/2 band together with two Q-branch lines in the (2)Σ(+) - (2)Π1/2 band. It is shown that this should lead to >70% of total population in the lowest rotational level at 300 K and over 99% at 77 K. In principle, the multiple Q-branch lines could be pumped with just two broad-band (∼Δν = 0.4-3 cm(-1)) infrared lasers.