A temperature grid is used for the description of motion in the hydrogen ionization region (HIR). This means zones are labeled by temperature rather than mass. Outside the HIR, the conventional Lagrangian grid is used, with transitional coordinates at the boundaries. Although our final object is to apply this scheme to the nonlinear periodic integration problem, we have first constructed a linear version as a test. It is found that periods and growth rates agree very well with those calculated using pure Lagrangian coordinates, but the temperature grid scheme proves less sensitive to a reduction of zones in the HIR. This property is desirable for the nonlinear problem where zoning must necessarily be coarse. As a further test of the temperature grid, we formulate the linear work integral in the new coordinates and confirm the consistency of the growth rates. Finally, it is shown that the scheme is insensitive to a change in the manner in which the transition zones are treated
