Hyperbolic temperature exposures (in which the rate of temperature rise increases with time) and an analytical solution to a rate-process model were used to characterise the impairment of respiration in samples containing both phloem (live bark) and vascular-cambium tissue during exposures to temperatures such as those experienced by the vascular cambium in tree stems heated by forest fires. Tissue impairment was characterised for red maple (Acer rubrum), chestnut oak (Quercus prinus), Douglas fir (Pseudotsuga menziesii), and ponderosa pine (Pinus ponderosa) samples. The estimated temperature dependence of the model’s rate parameter (described by the Arrhenius equation) was a function of the temperature regime to which tissues were exposed. Temperatures rising hyperbolically from near ambient (30°C) to 65°C produced rate parameters for the deciduous species that were similar at 60°C to those from the literature, estimated by using fixed temperature exposures. In contrast, samples from all species showed low rates of impairment, conifer samples more so than deciduous, after exposure to regimes in which temperatures rose hyperbolically between 50 and 60°C. A hypersensitive response could explain an early lag in tissue-impairment rates that apparently caused the differences among heating regimes. A simulation based on stem vascular-cambium temperature regimes measured during fires shows how temperature-dependent impairment rates can be used to predict tissue necrosis in fires. To our knowledge, hyperbolic temperature exposures have not been used to characterise plant tissue thermal tolerance and, given certain caveats, could provide more realistic data more efficiently than fixed-temperature exposures.