During the preliminary design stages, designers often have incomplete knowledge about the interactions among design parameters. We are developing a methodology that will enable designers to create models with levels of detail and accuracy that correspond to the current state of the design knowledge. The methodology uses Bayesian surrogate models that are updated sequentially in stages. Thus, designers can create a rough surrogate model when only a few data points are available and then refine the model as the design progresses and more information becomes available. These surrogates represent the system response when limited information is available and when few realizations of experiments or numerical simulations are possible. This paper presents a covariance-based approach for building surrogates in the preliminary design stages when bounds are not available a priori. We test the methodology using an analytical one-dimensional function and a heat transfer problem with an analytical solution, in order to obtain error measurements. We then illustrate the use of the methodology in a thermal design problem for wearable computers. In this problem, the underlying heat transfer phenomena make the system response non-intuitive. The surrogate model enables the designer to understand the relationships among the design parameters in order to specify a system with the desired behavior.