A one-dimensional thermo-electrical mathematical model describing the heating and cooling of thin Ni-Cr20% wires is presented. The model is applied for wires in a free air environment and to wires placed in small circular cavities formed by expanded polystyrene material. The basis of the model is a semicoupled solution of the heat conduction equation and the electrical diffusion equation in a one-dimensional (1-D) control volume finite-difference framework. A study on the available natural convection correlations for thin metal wires for Rayleigh numbers in the range of 10-3-101 is carried out in order to select an appropriate heat transfer coefficient for the time-dependent heating and cooling of a wire. The model is tested against experimental data and is found to be in a good agreement with previous investigations. Based on the findings, expressions for the heat transfer coefficient of a hot wire inside a small circular cavity are suggested.