In the evolving landscape of unconventional computing, this review explores the nascent field of thermal computing. Thermal computers, which use heat as a computational element, present a significant shift from traditional computing paradigms. This review focuses on memory devices and logic gates that function via heat transfer mechanisms, exploring thermal computing's potential to harness heat for computational purposes and expand the horizons of computing beyond conventional electronic paradigms. The motivation for this work stems from the need to expand the horizons of computing beyond conventional electronic systems-which have overshadowed all other forms of computing since the 20th century-leveraging the 72% of global primary energy lost in conversion processes. By harnessing the world's ample amounts of waste thermal energy, one can envisage computational advancements in diverse areas such as self-powered systems, extreme environmental applications, and server farms, wherein thermal computing devices could synergistically interact with electronic systems. To address the gap in comprehensive studies on thermal computing's engineering applicability and real-world integration, this review includes a detailed analysis of thermal memory devices and logic gates, evaluating their data retention, distinct states, and read/write speeds, alongside their scalability and potential real-world applications. A comprehensive technology readiness assessment for these devices underscores their potential and the challenges ahead in transitioning from theoretical constructs to practical tools. The outcomes of this assessment found that the Radiative Thermal Transistor score outperformed all other memory devices by 9.4% and the NanoThermoMechanical logic gates score outperformed other logic devices by 27%. To conclude, this review highlights the need for further advancement in thermal computing, underlining its potential to revolutionize computational models and expand the frontiers of information science. By integrating hysteresis and bistability with effective thresholding, thermal computing devices could provide stable, reliable, and efficient alternatives to electronic counterparts, leading to a seismic shift in computational technologies.