Computational Colour Constancy (CCC) consists of estimating the colour of one or more illuminants in a scene and using them to remove unwanted chromatic distortions. Much research has focused on illuminant estimation for CCC on single images, with few attempts of leveraging the temporal information intrinsic in sequences of correlated images (e.g., the frames in a video), a task known as Temporal Colour Constancy (TCC). The state-of-the-art for TCC is TCCNet, a deep-learning architecture that uses a ConvLSTM for aggregating the encodings produced by CNN submodules for each image in a sequence. We extend this architecture with different models obtained by (i) substituting the TCCNet submodules with C4, the state-of-the-art method for CCC targeting images; (ii) adding a cascading strategy to perform an iterative improvement of the estimate of the illuminant. We tested our models on the recently released TCC benchmark and achieved results that surpass the state-of-the-art. Analyzing the impact of the number of frames involved in illuminant estimation on performance, we show that it is possible to reduce inference time by training the models on few selected frames from the sequences while retaining comparable accuracy.