Many self-accelerating decomposition temperatures (SADTs) of solid organic peroxides and self-reactive substances have been determined with the UN test method HA which is a scaled down test in a small Dewar vessel. For solid organic peroxides and solid self-reactive substances Fierz has questioned this procedure in a recent paper. Fierz concluded that the Dewar test results should not be extrapolated to beyond 81 packages, owing to the thermal insulation value of solids. On the other hand. long term experience with the test, with a great variety of solid organic peroxides and self-reactive substances show about equal critical temperatures in the small Dewar vessel and on 50 kg scale. In the present work, we first checked, by numerical simulations, the Dewar scale versus the larger scale. in a way comparable with Fierz' method: both scales are simulated by spheres. consisting of a number of annular layers, for the large scale the usual external heat loss term is used but for the small scale the outside heat transfer is strongly limited. The outcome of these simulations, Covering a variety of physical parameters. supports the concerns expressed by Fierz. After this. we performed accurate cooling and heating experiments with solid oraganic peroxide in the usual Dewar vessel, provided with a large set of thermocouples. The results of these experiments showed that the simulation model for the Dewar vessel has to be changed from a spherical analogue to a short cylinder of solid material with heat exchange mainly via its top (U-top similar to 3.5 W/(m(2) K), overall heat transfer coefficient) and some heat exchange (U-side similar to 029 W/(m(2) K)) through its cylindrical and bottom part. With this "modified cylinder" model (being neither an infinitely long cylinder nor a slab) of the Dewar vessel, we found that the UN method HA enables an accurate prediction of the SADT, with small deviations of 0 +/-2.5degreesC. Further. by performing a truly three-dimensional (3D) finite element calculation in FEMLAB, the new heat characteristics of the Dewar vessel as well as a 50 kg package of dilauroyl peroxide. a solid organic peroxide. were checked. The outcome was compared with the critical ambient temperatures known for various package sizes. which agreed well. (C) 2004 Elsevier B.V. All fights reserved.