We present the first application of the unbiased exponential resummation method to the determination of the QCD pseudocritical temperature Tpc at vanishing baryon chemical potential µB. By reconstructing the finite-density baryon number susceptibility χ^B_2, we define two thermal-derivative observables whose peak positions yield T^T_pc = 160.2(4)(3) MeV and T^C_pc = 158.1(5)(3) MeV. We also show that the pseudocritical temperature T^χ_pc obtained from the peak of the fourth-order baryon number susceptibility χ^B_4 is consistent with these determinations and with previous lattice-QCD results based on Taylor expansions. Further, we demonstrate that scaling relations between χ^B_4 and the thermal derivatives of χ^B_2 yield mutually consistent estimates of the leading second order curvature coefficient κ^B_2 at the corresponding pseudocritical temperatures. A direct analysis of the µB dependence of the pseudocritical temperatures provides an independent but substantially less constrained determination of the curvature, which remains statistically consistent with the scaling-based estimates. These results demonstrate the consistency of unbiased exponential resummation with the expected scaling behavior and establish it as a complementary approach for probing the QCD crossover at small finite baryon density.