The steady-state thermal resistance of a small heat source applied to a diamond heat spreader attached to a larger substrate with Newtonian cooling on the opposite side was evaluated using numerical simulation. The substrate with Newtonian cooling models a range of convection-cooled designs, such as a heat sink base with a finned surface or the base of a cold plate with liquid cooling. The objective of this work is to quantify the thermal performance of the modeled system as a function of the diamond heat spreader size and properties. The resulting maximum thermal resistance as a function of diamond spreader thickness, lateral dimension, and conductivity are presented, as well as some guidelines for effective thermal design. In addition, a range of convection conditions typical for these applications are examined. Synthetic diamond is still an expensive material, ranging from $1 to $20 per square millimeter in the lateral plane. The price increases sharply with conductivity, thickness, and lateral dimension, all of which increase thermal performance of the diamond spreader. For this reason, the cost per thermal performance is a distinctly different optimization problem from the thermal performance alone. The results of this optimization are presented for a Biot number typical for forced convection through a finned surface using direct air cooling.