Slow pulsed capillary discharges are under investigation for use as plasma channel waveguides in laser-wakefield acceleration. In this study, we present a non-local thermal equilibrium (non-LTE) plasma model with a model for the wall temperature coupled to it. This model is used to describe an example of a slow pulsed capillary discharge, and the results are compared with experimental results. The agreement is satisfactory, indicating suitability of our model. Significant deviations from LTE are found during the formation of the plasma channel. The model is also used to study the influence of the discharge current on the guiding properties. It was found that this influence is small over most of the current range that was investigated.