A nonlinear least‐squares curve‐fitting routine has been used to analyze single‐tip Langmuir probe measurements from the Tandem Mirror Experiment Upgrade during high‐density (≊1×1012cm−3) operation. This procedure provided estimates of uncertainties (variances) in the electron temperature and plasma density due to noise in the probe current. The electron temperature and plasma potential inferred from the fit were found to increase with the upper cutoff voltage used above a certain voltage. This effect appears to be due to a departure of the electron current from an exponentially increasing function for probe positions inside the limiter radius only. The fitted values for electron temperature and plasma density are consistent with previous measurements obtained with a double‐tipped probe and the fitted values of space potential indicate a linear relationship with electron temperature.