Analysis of spatial panel data is of great importance and interest in spatial econometrics. Here we consider cigarette demand in a spatial panel of 46 states of the US over a 30-year period. We construct a demand equation to examine the elasticity of per pack cigarette price and per capita disposable income. The existing spatial panel models account for both spatial autocorrelation and state-wise heterogeneity, but fail to account for temporal autocorrelation. Thus we propose new spatial panel models and adopt a fully Bayesian approach for model parameter inference and prediction of cigarette demand at future time points using MCMC. We conclude that the spatial panel model that accounts for state-wise heterogeneity, spatial dependence, and temporal dependence clearly outperforms the existing models. Analysis based on the new model suggests a negative cigarette price elasticity but a positive income elasticity. The methodology presented here may be suitable for spatial-temporal lattice data in general.