State space models with time-varying parameters have been used to model processes displaying variations at a variety of temporal scales. We develop such models with the goal of forecasting hemispherically averaged surface temperatures at interannual time scales. To capture variations on several scales, we formulate hierarchical models for the main processes of interest conditional upon model coefficients and variances that are themselves modeled via state space models. These parameter models are allowed to have different and unknown time scales. Further, the use of covariates can aid in modeling these time-varying covariates. Bayesian inference, including model selection, for such models is discussed. Special issues in forecasting based on models with unknown future covariates are discussed and illustrated in forecasting hemispheric surface temperatures. Copyright © 2012 John Wiley & Sons, Ltd.