Coulomb-driven renormalization of electronic spectra in monolayer transition-metal dichalcogenides (TMDCs) remains poorly understood at finite temperature. Using the Rytova-Keldysh potential with a nonlocal dielectric response, we calculate quasiparticle band-gap renormalization (BGR) and the Fermi-edge absorption spectrum over experimentally relevant carrier densities and temperatures. Exchange and correlation self-energies are treated successively within Hartree-Fock (HF), the random-phase approximation (RPA), and the Hubbard local-field approximation (HFA). Only the HFA, which embeds the $G\left(q\right)$ local-field factor, reproduces recent temperature- and density-resolved measurements: it broadens the band gap at low densities and produces a density-induced redshift of the Fermi absorption edge through enhanced screening. The same framework accounts for the nonmonotonic BGR observed in cyclotron resonance experiments on disordered monolayers when disorder-induced thermal broadening is included. The results establish a local-field-corrected many-body theory as the minimal quantitative description of carrier-doped TMDCs and provide a roadmap for engineering interaction-driven electronic phases in two dimensions.

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• Band gap
• Dielectric properties
• Fermi surface
• Plasmons
• Transition metal dichalcogenides
• Hartree-Fock methods
• Random phase approximation