Temperature \(T\) is the intensive thermodynamic variable conjugate to energy that characterizes a system in thermal equilibrium with a heat bath. In Statistical Mechanics it enters through the Boltzmann factor \(e^{-\beta H}\) with the inverse temperature
In natural units (\(k_B=1\)) temperature has units of energy, and it is the workhorse variable of thermal field theory.
The key identity of finite-temperature QFT is that the inverse temperature equals the extent of Euclidean time. Because the partition function is \(Z=\mathrm{Tr}\,e^{-\beta H}\) and \(e^{-\beta H}\) is imaginary-time evolution over an interval \(\beta\), the euclidean time direction is compactified on a circle of circumference
High temperature \(\Leftrightarrow\) short Euclidean time extent \(\beta\to 0\); zero temperature \(\Leftrightarrow\) \(\beta\to\infty\). On the lattice with \(N_\tau\) temporal sites of spacing \(a\), the temperature is set geometrically by
Raising \(T\) drives QCD through a deconfinement/chiral transition (a crossover near \(T_c\approx 155\) MeV at zero density): below \(T_c\) quarks and gluons are confined into hadronic bound states; above it they form a quark–gluon plasma. Mapping this transition and the equation of state as a function of temperature is a principal aim of lattice QCD at finite temperature, and it connects to heavy-ion collisions and early-universe cosmology.