The paper investigates the transition temperature ($T_c$) of Quantum Chromodynamics (QCD) using Symanzik improved gauge and stout-link improved staggered fermionic lattice simulations. Physical quark masses for both light ($m_{ud}$) and strange ($m_s$) quarks are used, with four lattice spacings ($N_t$=4,6,8,10) to perform a continuum extrapolation. Only $N_t$=6,8,10 are suitable for controlled extrapolation, while $N_t$=4 is out of the scaling region. Since the QCD transition is a crossover, different observables yield different numerical $T_c$ values. The peak of the renormalized chiral susceptibility predicts $T_c$=151(3)(3) MeV, while $T_c$ values based on the strange quark number susceptibility and Polyakov loops are 24(4) MeV and 25(4) MeV higher, respectively. The non-vanishing width of the peaks even in the thermodynamic limit is also determined. The study aims to eliminate limitations in previous analyses, such as unphysical spectra and scale setting, and provides a full result for the $T \neq 0$ transition, though other lattice fermion formulations are needed for cross-checking.The paper investigates the transition temperature ($T_c$) of Quantum Chromodynamics (QCD) using Symanzik improved gauge and stout-link improved staggered fermionic lattice simulations. Physical quark masses for both light ($m_{ud}$) and strange ($m_s$) quarks are used, with four lattice spacings ($N_t$=4,6,8,10) to perform a continuum extrapolation. Only $N_t$=6,8,10 are suitable for controlled extrapolation, while $N_t$=4 is out of the scaling region. Since the QCD transition is a crossover, different observables yield different numerical $T_c$ values. The peak of the renormalized chiral susceptibility predicts $T_c$=151(3)(3) MeV, while $T_c$ values based on the strange quark number susceptibility and Polyakov loops are 24(4) MeV and 25(4) MeV higher, respectively. The non-vanishing width of the peaks even in the thermodynamic limit is also determined. The study aims to eliminate limitations in previous analyses, such as unphysical spectra and scale setting, and provides a full result for the $T \neq 0$ transition, though other lattice fermion formulations are needed for cross-checking.