•Dynamic instability of temperature-dependent FG nanobeam subjected to an axially oscillating loading as well as magnetic field in thermal environment is explored.•The governing equilibrium equations are obtained according to the nonlocal strain gradient theory (NSGT) in conjunction with Timoshenko beam theory (TBT).•Navier in conjunction with bolotin methods are applied for obtaining dynamic instability region (DIR) of the FG nanobeam.•The influences of various noticeable factors such as temperature variation, length to thickness ratio, nonlocal parameter (NP), static load factor, length scale parameter (LSP), power-law index as well as magnetic field on the dynamic instability behavior of FG nanobeam are carefully examined. Dynamic instability of temperature-dependent TIMOSHENKO functionally graded (TFG) nanobeam exposed to an axial excitation load and magnetic field in thermal environment is carried out in the present work. The power-law model is utilized to represent the material variations across the nanobeam thickness. In accordance with nonlocal strain gradient theory (NSGT), the equations of motion are derived through Hamilton's principle. Navier and Bolotin's approaches are here employed in order to specify the dynamic instability region of the FG nanoscale beam. The effects of different factors like length to thickness ratio, temperature variation, nonlocal parameter (NP), power-law index, static load factor, magnetic field as well as length scale parameter (LSP) on the dynamic instability boundary are scrutinized through some parametric studies. Based on the outcomes, with increasing temperature change, power-law index and NP, the instability region will be happened at lower pulsation frequencies whereas LSP and magnetic field effects are on the contrary. The obtained results can be useful as reference solutions for future dynamic stability analysis of FG nanobeams reinforced nanocomposites under thermal and magnetic effects. Display omitted