An integral equation governing an instability due to ion temperature gradients is derived. In the presence of magnetic shear, localized non‐convective normal modes of instability are shown to exist if the relative temperature gradient is larger than that of density, unless the shear is exceedingly strong, i.e., the field shears through a large angle in the distance in which the temperature drops. Quasi‐modes which are less localized in the direction of the gradient can be constructed from these normal modes and a large thermal diffusion may be expected. Conversely the mass diffusion is shown to be rather slow so that it is reasonable to assume that an effective ``divertor'' should keep the actual heat loss quite small.