This paper presents a method to transform procedural sashiko embroidery into intricately coloured polygonal tiles. Two-coloured hitomezashi stitch patterns are used as time-periodic inputs to the heat diffusion equation. Rendering the resulting temperature field with a photograph as colour wheel produces decorative rectangular tiles. Conformal Schwarz-Christoffel mappings extend the recipe to both regular and irregular polygons of arbitrary vertex count. A range of tile designs and examples of an Archimedean and Cairo tessellation thereof are showcased.