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We demonstrate that the profile of the space-resolved spectral function atfinite temperature provides a signature of Wigner localization for electrons inquantum wires and semiconducting carbon nanotubes. Our numerical evidence isbased on the exact diagonalization of the microscopic Hamiltonian of fewparticles interacting in gate-defined quantum dots. The minimal temperaturerequired to suppress residual exchange effects in the spectral function imageof (nanotubes) quantum wires lies in the (sub-) Kelvin range.

Spectral function of few electrons in quantum wires and carbon nanotubes as a signature of Wigner localization