Given that the reionization history of cosmic hydrogen is yet to be stringently constrained, it is worth checking the prospects of doing so using physically motivated models and available observational data. For this purpose, we use an extended version of the explicitly photon-conserving semi-numerical model of reionization, SCRIPT, which also includes thermal evolution of the intergalactic medium (IGM). The model incorporates the effects of inhomogeneous recombination and radiative feedback selfconsistently and is characterized by five free parameters (two for the redshift-dependent ionization efficiency, two for the ionizing escape fraction, and another for reionization temperature increment). We constrain these free parameters by simultaneously matching with various observational probes, e.g., estimates of the ionized hydrogen fraction, the CMB scattering optical depth and the galaxy UV luminosity function. In addition, we include the low-density IGM temperature measurements obtained from Lyman-𝛼 absorption spectra at 𝑧 ∼ 5.5, a probe not commonly used for Bayesian analysis of reionization parameters. We find that the interplay of the various data sets, particularly inclusion of the temperature data, leads to tightening of the parameter constraints. Our default models prefer a late end of reionization (at 𝑧 6), in agreement with other recent studies. We can also derive constraints on the duration of reionization, Δ𝑧 = 1.81 +0.51 −0.67 and the midpoint of reionization, 𝑧 mid = 7.0 +0.30 −0.40 . The constraints can be further tightened by including other available and upcoming data sets.