We study the cosmological constraints on unparticle interactions and the temperature of the Universe for the case where unparticle states can be modelled as continuous mass particles with lifetime 1s. By considering thermal background quark decay to continuous mass scalars via a scalar operator of dimension dU, we show that the condition that the Universe is not dominated by scalars at nucleosynthesis imposes a lower bound on the scale of the interaction of the unparticle sector, with MU 20−2600 TeV for ΛU 1 TeV, 1.1 ≤ dU ≤ 2.0 and 2 ≤ dBZ ≤ 4. The existence of a long-lived scalar sector also imposes an upper bound on the temperature of the Universe during radiation-domination, which can be as low as a TeV for MU close to its lower bound.