We explore the possibility of having baryogenesis at temperatures below any dilution mechanism, such as inflation or sphaleron effects at the electroweak transition. We find that large infrared CPT violation (CPTV) effects are a necessary ingredient for such a baryogenesis. We give an explicit example of a theory supporting this scenario at the kinematical level in which such CPTV effects are suppressed at the level of CPT tests based on mass differences between particle and antiparticle.