Using (2712.4 ± 14.3) x 10⁶ ψ(3686) events collected with the BESIII detector operating at the BEPCII collider, we search for the hadronic transition h_c → π⁺π^-J/ψ via ψ(3686) → π⁰h_c. No significant signal is observed. We set the most stringent upper limits to date on the branching fractions B(ψ(3686) → π⁰h_c) x B(h_c → π⁺π^-J/ψ) and B(h_c → π⁺π^-J/ψ) at the 90% confidence level, which are determined to be 6.7 x 10^-7 and 9.4 x 10^-4, respectively.