Heat treatment of milk for hygiene and preservation is carried out in energy integrated pasteurisers units which include several plate heat exchangers (PHEs), a holding tube and ancillary piping. Fouling reduces energy efficiency and cleanings generate downtime and wastes. No detailed dynamic models are currently available of full heating-cleaning cycles for an overall unit. Using a first principle modelling approach, a 2D dynamic thermal model, coupled with semi-mechanistic fouling and cleaning in place (CIP) models, is developed for the whole pasteurisation process, and used to test various heating-cleaning cycles. The model generality and flexibility are demonstrated for high temperature short time (HTST) and ultra-high temperature (UHT) treatments. The whole unit thermal model is validated against experimental data for a HTST process, with excellent agreement. Fouling evolution, distribution and impact are assessed for both processes. A UHT heating-cleaning cycle simulation enables quantifying the amounts of cleaning agent and waste water produced. The new model is suitable for control, optimisation of heating and cleaning strategies, and waste reduction studies.