Linear temporal stability analysis of a viscous liquid jet in ambient gas under a thermal field is performed, considering both axisymmetric and nonaxisymmetric disturbances. The basic temperature profile is analytically derived from the thermal conduction equation. The thermal field influences the jet instability characteristics through thermal-capillary and Marangoni effects by changing the stress at the jet surface. Two unstable modes are stimulated under the thermal field, including varicose and helical modes. The energy budget analysis reveals that the helical mode is induced by the azimuthal Marangoni instability. The influences of Marangoni effect and thermal diffusivity on the nonisothermal jet instability are studied systematically. The enhancement of the Marangoni effect (increasing the Ma) or the suppression of the thermal diffusivity effect (increasing the Pr) will promote the helical mode and make it dominate the jet instability. As the dominant mode changes from varicose mode to helical mode, the dominant instability mechanism changes from the Rayleigh-Plateau instability to the azimuthal Marangoni instability synchronously. Phase diagrams of different dominant modes and instability mechanisms are represented in the $(\mathrm{Pr},\mathrm{Ma})$ plane with varying inertial stress. The enhancement of the inertial effect will decrease the critical Ma and Pr for the transition from varicose mode to helical mode, which encourages the helical mode to dominate the jet instability.

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• Instability of free-surface flows
• Surface tension effects
• Thermocapillarity
• Wakes & jets