The behavior of heat transfer processes in engineering and physical systems is profoundly influenced by domain geometry and the internal structure of temperature fields. As modern applications, such as compact heat exchangers, microelectronics, and additive manufacturing, require increasingly complex geometries and fine control over thermal behavior, traditional numerical methods often struggle with domain definition, boundary enforcement, and visualization. The theory of R-functions, developed by V.L. Rvachev, provides a powerful analytical tool for representing complex domains through logical combinations of implicit functions. This paper explores the integration of R-functions with lightweight browser-based computation, using JavaScript to model and visualize heat transfer domains in two dimensions. The proposed method supports the analytical construction of geometric domains and exact boundary conditions through R-operations, implemented in a modular and computationally efficient manner. The function visualization pipeline is structured in three main stages: domain pre-processing with extrema detection, annotation and level curve configuration, and real-time pixel-based rendering. Optimization through minimal-index R-operations allows fast computation, enabling interactive visualization directly in a web browser with sub-second response times. As a case study, the level curves of a heat transfer problem involving a porous square cavity with four heated cylinders are rendered in real time, demonstrating the method’s speed and flexibility. The framework supports interactive manipulation of geometric parameters, making it valuable for parametric studies, design optimization, and educational purposes. The approach is accessible, platform-independent, and requires no specialized software, offering a powerful alternative to traditional simulation workflows in heat transfer and related fields.