In MRI, the dynamics of gradient fields can be predicted by assuming that the system is linear and time-invariant. However, time-invariance can be violated by thermal effects. To address this shortcoming, it has been proposed to expand the GIRF model by thermal variation parametrized with the help of temperature sensors. It has remained open how many relevant thermal degrees of freedom the system actually had and where the matching number of sensors should be placed to capture them. In the present work, we address these questions using infrared photography and principal component analysis of gradient heating. Response modelling is additionally enhanced by accelerating GIRF measurements and including cross-terms. The improvements are shown in the prediction of gradient waveforms for image reconstruction and in the effects on the images.