A screen assembly has a material that conforms to the borehole shape after insertion. The assembly comprises a compliant layer that takes the borehole shape on expansion. The outer layer is formed having holes to permit production flow. The selected conforming material swells with heat, and in one non-limiting embodiment comprises a shape memory foam that is thermoset or thermoplastic. Heat is provided by supplying a fuel (including an oxidant) to a catalyst in close proximity to the compliant layer so that the product from the catalytic reaction is heated steam which contacts and deploys the conforming material. The base pipe can have a screen over it to act as an underlayment for support of the conforming layer or alternatively for screening.