The ensemble Kalman filter has obtained popularity for field estimation, in particular for updating of reservoir simulation models. Here we will present a through study on the effect of the ensemble size. To be able to run a large number of simulations, we have simplified the modeling by focusing on the heat equation, but will also include a discussion on what to expect for reservoir simulation models. We find that a modest ensemble size is enough to match the measurements, but the ensemble size has to be increased significantly to get a proper picture of the model uncertainty.