The Multiplicative Random Cascade (MRC) disaggregation model has been extensively used to disaggregate precipitation in many regions across the globe. In this study, it is adapted to disaggregate a range of climate variables (CV) relevant for hygrothermal modelling of building envelopes. This generalized MRC-G model is further improved by explicitly modelling the cross-correlation structure between CVs in the MRC-G-CV model. A thorough evaluation of MRC, MRC-G, and MRC-G-CV models is performed for five Canadian cities: Ottawa, Vancouver, Calgary, St. Johns, and Winnipeg. Results indicate that the MRC model is able to simulate grid-level statistics with >90% accuracy. Grid-level extreme magnitudes and spatial cross-correlation structures are also well simulated. Error magnitudes associated with hourly predictions indicate superior performance of the models in respect to thermal variables, followed by wind variables, and then moisture related variables. Finally, the performance of MRC-G model towards modelling cross-correlation among CVs is found to improve by >50% in terms of energy distance by explicitly modelling these relationships in the MRC-G-CV model. Results indicate that the MRC model variants demonstrated in this study have the potential to facilitate effective hygrothermal performance evaluation of building envelopes at locations where observational sub-daily climate records are unavailable.