Instant-freezing methods inaccurately predict transient thermal stresses in rapidly cooling silicate glass plates because of the temperature dependent rheology of the material. The temperature dependent rheology of the lithosphere may affect the transient thermal stress distribution in a similar way, and for this reason we use a thermoviscoelastic model to estimate thermal stresses in young oceanic lithosphere. This theory is formulated here for linear creep processes that have an Arrhenius rate dependence on temperature. Our results show that the stress differences between instant freezing and linear thermoviscoelastic theory are most pronounced at early times (0-20 m.y. when the instant freezing stresses may be twice as large. The solutions for the two methods asymptotically approach the same solution with time. A comparison with intraplate seismicity shows that both methods underestimate the depth of compressional stresses inferred from the seismicity in a systematic way. -from Authors