The early X-ray afterglows of gamma-ray bursts (GRBs) are usually well described by absorbed power laws. However, in some cases, additional thermal components have been identified. The origin of this emission is debated, with proposed explanations including supernova shock breakout, emission from a cocoon surrounding the jet, as well as emission from the jet itself. A larger sample of detections is needed in order to place constraints on these different models. Here we present a time-resolved spectral analysis of 74 GRBs observed by Swift XRT in a search for thermal components. We report six detections in our sample, and also confirm an additional three cases that were previously reported in the literature. The majority of these bursts have a narrow range of blackbody radii around ∼ 2 × 10 12 cm, despite having a large range of luminosities (L peak ∼ 10 47 − 10 51 erg s −1 ). This points to an origin connected to the progenitor stars, and we suggest that emission from a cocoon breaking out from a thick wind may explain the observations. For two of the bursts in the sample, an explanation in terms of late prompt emission from the jet is instead more likely. We also find that these thermal components are preferentially detected when the X-ray luminosity is low, which suggests that they may be hidden by bright afterglows in the majority of GRBs.