An hourly water temperature time series recorded the Gairn catchment (Scotland) is considered here along with seven covariates (flow, air temperature, rainfall, wind speed, wind direction, radiation, and soil temperature). Due to its high complexity, the dynamics of the water temperature is analysed through non-homogeneous Markov switching autoregressive models (MSRAMs) in order to tackle the non-linearity, non-Normality, non-stationary, and long memory of the series. MSARMs are observed state-dependent autoregressive processes driven by an unobserved, or hidden, Markov chain. In this paper, MSARMs are proposed within the Bayesian framework. Bayesian inference, model choice, and stochastic variable selection are performed numerically by Markov chain Monte Carlo algorithms. Hence, it is possible to efficiently fit the actual data, reconstruct the sequence of hidden states, restore the missing values, classify the observations into a few regimes, select the covariates that drive both the observed and the hidden process providing new insight on the water temperature dynamics. Our proposal is very general and flexible and can be applied to any kind of environmental time series.