The influence of heat accumulation on surface roughness during powder-bed additive manufacturing was investigated. A series of Ti-6Al-4V thin plates were produced by using an identical heat input by electron beam melting® (EBM). Spacing distances of 5 mm, 10 mm, and 20 mm were used. The surface roughness of as-built thin plates was measured using a two-axis profilometer. A numerical model was developed to study the influence of spacing distance on heat accumulation. An inverse relationship between the spacing distance and surface roughness was revealed. The experimental and numerical results showed that the surface quality of buildups could be controlled not only by process parameters, but also by the arrangement of components in the buildup chamber. At a constant spacing distance, an increase in the number of powder layers resulted in the accumulation of more heat between the thin plates. An increase in the spacing distance resulted in an upward translation of the Bearing Area Curve (BAC) toward shallower depths, with a reduced core roughness depth (Rk) and peak height (Rpk). A logarithmic regression equation was established from the experimental data. This equation could be used to predict the surface roughness of parts fabricated by EBM® in the studied range of spacing distances.