The physical properties of hole-doped cuprate high-temperature superconductors are heavily influenced by an energy gap known as the pseudogap whose origin remains a mystery second only to that of superconductivity itself. A key question is whether the pseudogap closes at a temperature T*. The absence of a specific heat anomaly, together with persistent entropy losses up to 300K, have long suggested that the pseudogap does not vanish at T*. However, amid a growing body of evidence from other techniques pointing to the contrary we revisit this question. Here we investigate if, by adding a temperature dependence to the pseudogap energy and quasiparticle lifetime in the resonating-valence-bond spin-liquid model of Yang Rice and Zhang, we can close the pseudogap quietly in the specific heat.