The engineering limits of plasma-facing components (PFCs) constrain the allowable operational space of tokamaks. Poorly managed heat fluxes that push the PFCs beyond their limits not only degrade core plasma performance via elevated impurities, but can also result in PFC failure due to thermal stresses or melting. Simple axisymmetric assumptions fail to capture the complex interaction between three-dimensional (3-D) PFC geometry and two-dimensional or 3-D plasmas. This results in fusion systems that must either operate with increased risk or reduce PFC loads, potentially through lower core plasma performance, to maintain a nominal safety factor. High-precision 3-D heat flux predictions are necessary to accurately ascertain the state of a PFC given the evolution of the magnetic equilibrium. A new code, the Heat flux Engineering Analysis Toolkit (HEAT), has been developed to provide high-precision 3-D predictions and analysis for PFCs. HEAT couples many otherwise disparate computational tools together into a single open-source python package. Magnetic equilibrium, engineering computer-aided design, finite volume solvers, scrape-off layer plasma physics, visualization, high-performance computing, and more, are connected in a single web-based user interface. Linux users may use HEAT without any software prerequisites via an appImage. This paper introduces HEAT, discusses the software architecture, presents the first HEAT results, and outlines physics modules in development.