Since the advent of modern electronics technology, heat transfer science and engineering has served in the development of computer technology. The computer as an object of heat transfer research has a unique aspect; it undergoes morphological transitions and diversifications in step with the progress of microelectronics technology. Evolution of computer's hardware manifests itself in increasing packing density of electronic circuits, modularization of circuit assemblies, and increasing hierarchical levels of system internal structures. These features are produced by the confluence of various factors; the primary factors are the pursuit of ever higher processing performance, less spatial occupancy, and higher energy utilization efficiency. The cost constraint on manufacturing also plays a crucial role in the evolution of computer's hardware. Besides, the drive to make computers ubiquitous parts of our society generates diverse computational devices. Concomitant developments in heat generation density and heat transfer paths pose fresh challenges to thermal management. In an introductory part of the paper, I recollect our experiences in the mainframe computers of the 1980s, where the system's morphological transition allowed the adoption of water cooling. Then, generic interpretations of the hardware evolution are attempted, which include recapturing the past experience. Projection of the evolutionary trend points to shrinking space for coolant flow, the process commonly in progress in all classes of computers today. The demand for compact packaging will rise to an extreme level in supercomputers, and present the need to refocus our research on microchannel cooling. Increasing complexity of coolant flow paths in small equipment poses a challenge to a user of computational fluid dynamics (CFD) simulation code. In highly integrated circuits the paths of electric current and heat become coupled, and coupled paths make the electrical/thermal codesign an extremely challenging task. These issues are illustrated using the examples of a consumer product, a printed circuit board (PCB), and a many-core processor chip.