  The possibility that population III stars have reionized the Universe at
redshifts greater than 6 has recently gained momentum with WMAP polarization
results. Here we analyse the role of early dust produced by these stars and
ejected into the intergalactic medium. We show that this dust, heated by the
radiation from the same population III stars, produces a submillimetre excess.
The electromagnetic spectrum of this excess could account for a significant
fraction of the FIRAS (Far Infrared Absolute Spectrophotometer) cosmic far
infrared background above 700 micron. This spectrum, a primary anisotropy
($\Delta T$) spectrum times the $\nu^2$ dust emissivity law, peaking in the
submillimetre domain around 750 micron, is generic and does not depend on other
detailed dust properties. Arcminute--scale anisotropies, coming from
inhomogeneities in this early dust, could be detected by future submillimetre
experiments such as Planck HFI.
