A zonally averaged energy balance climate model is used to generate zonal temperature variability through fluctuating meridional energy transports. In the base model, stochastic transport fluctuations are introduced by multiplying the eddy diffusion coefficients by Gaussian random deviates. For eddy coefficient variability of 50%, the base model generates an interannual temperature variability of 0.03 K for the global temperature, and 0.04 and 0.05 K for the Northern and Southern Hemispheric temperatures, respectively. The sensitivity to modeling assumptions of the model generated variability and its meridional distribution are investigated through a series of numerical experiments. For the range studied, the temperature variability level generated is linearly related to the transport variability level introduced. Switching from the multiplicative noise model of the base to an additive noise model results in an increase in the level of model generated temperature variability and a change in the shape of variance spectra of temperature anomaly time series. These model results are compared with a time series of central England temperatures as well as GCM generated climate variability. Because the level of variability is so dependent on the form of stochastic forcing parameterization, we conclude that great caution is needed before ascribing physical reality to such stochastic fluctuations.