Evolution of the internal temperature T and the chemical imbalance η_npe for a 1.68 M_⊙ star without muons built with the BPAL21 EOS (Prakash et al. 1988), with the initial conditions T = 10⁸ K and η_npe = 0. The spin-down is assumed to be caused by magnetic dipole radiation, with dipolar field strength B = 2.8 × 10⁸ G and initial period P₀ = 1 ms. The dashed lines are the quasi-steady state solution calculated from . In all cases, the protons are taken to be non-superfluid, while the neutron superfluid energy gaps are Δ_n = 0.01 MeV (upper left panel), Δ_n = 0.03 MeV (lower left panel), and Δ_n = 0.05 MeV (upper and lower right panels). The lower right panel shows a close-up of the second peak in temperature of the evolution plot shown in the upper right panel (Δ_n = 0.05 MeV) with a linear scale in time.