Material making studied under directional solidification considers a sample pulled longitudinally along a thermal gradient. In many experiments, it has however been observed the presence of transverse thermal gradients. The aim of this contribution is to investigate various mechanisms leading to this feature. The first part (or static part) considers the oven itself and presents theoretical estimates of transverse thermal gradients due to a non-ideal oven. Two situations are investigated: (a) the zone between heating and cooling devices is not large compared with sample thickness and (b) the latter zone is actually not adiabatic. The second part (or dynamic part) treats of another mechanism leading to transverse effects: differential heat transfer between sample and walls of confinement is investigated. When wall conductivity is large, heat extraction ceases to exclusively occur along the sample longitudinal axis and results in temperature gradients perpendicular to the direction of pulling. For the sake of deriving theoretical estimate, we investigate the following limit situation: the walls act as a thermal shunt; this in fact gives an upper bound to the departures to longitudinal temperature field, induced either by heat released from the bulk or latent heat rejected at the liquid-solid interface. In the third part of the paper, we investigate the strength of the convective motion that can be induced on the ground by such thermal gradients. Special attention is devoted to upward vertical Bridgman solidification. Comparison with solute convection intensity is performed in terms of orders of magnitude. (C) 2002 Elsevier Science B.V. All rights reserved.