The vibrational state of a glass is naturally incompatible with its configurational state, which makes the glass structurally unstable. When a glass is kept at constant temperature, both the vibrational and configurational states of a glass change with time until it becomes metastable (equilibrium) liquid and the two states become compatible. The process, known as structural relaxation, occurs at a progressively higher rate during heating, and the properties of a glass change accordingly. We add to this incompatibility by depressurizing a glass that had been formed by cooling a liquid under a high pressure, p, and then investigate the effects of the added incompatibility by studying thermal conductivity, κ, and the heat capacity per unit volume ρCp of the depressurized glass.We use glycerol for the purpose and study first the changes in the features of κ and of ρCp during glass formation oncooling under a set of different p. We then partially depressurize the glass and study the effect of the p-induced instability on the features of and Cp as the glass is isobarically heated to the liquid state.At a given low p, the glass configuration that was formed by cooling at high-p had a higher κ than the glass configuration that was formed by cooling at a low p. The difference is more when the glass is formed at a higher p and/or is depressurized to a lower p. On heating at a low p, its κ decreases before its glass-liquid transition range is reached. The effect is the opposite of the increase in observed on heating a glass at the same p under which it was formed. It is caused by thermally assisted loss of the added incompatibility of configurational and vibrational states of a high-p formed glass kept at low p. If a glass formed under a low-p is pressurized and then heated under high p, it would show the opposite effect, i.e., its κ would first increase to its high p value before its glass-to-liquid transition range.