The scarcity of clean water and the lack of sustainable cooling systems are continuously pressing. Although many technologies are well-established, such as vapour compression for refrigeration and reverse osmosis for desalination, they are energy-intensive and conventional refrigeration technology utilising working fluids of long-lasting ozone-depleting and greenhouse effects. Alternatively, adsorption and absorption technologies can meet such demands, and they are the most feasible to utilise the waste and renewable heat abundant in many locations. Therefore, this paper computationally studies the emerging integrated adsorption-absorption system for cooling cum desalination employing transient waste heat sources of various waveform characteristics. A previously validated computational model for the adsorption subsystem was coupled with a thermodynamic model for the absorption subsystem and experimental heat profiles obtained from an internal combustion engine. The energy and exergy analysis of the integrated system utilising the actual heat source from an internal combustion engine and predefined waveforms were undertaken and benchmarked against that operated under steady heat sources. The integrated system operated with a relatively low exergy efficiency in the absorption cycle of up to 15.33%. The adsorption bottoming cycle successfully utilised the heat from the absorption subsystem at a relatively higher exergy efficiency of up to 42.69%. The execution of a transient heat source of sinusoidal waveform enhanced the water production by up to 30% and the cooling of absorption and adsorption subsystems by 24% and 15%, respectively. However, admitting realistic waveforms of an internal combustion engine showed marginal differences compared to the steady heat sources owing to their high frequencies and small amplitudes.