Wavefront coding involves the insertion of an asymmetric refractive mask close to the pupil plane of an imaging system so as to encode the image with a specific point spread function that, when combined with decoding of the recorded image, can enable greatly reduced sensitivity to imaging aberrations. The application of wavefront coding has potential in the fields of microscopy, where increased instantaneous depth of field is advantageous and in thermal imaging where it can enable the use of simple, low-cost, light-weight lens systems. It has been previously shown that wavefront coding can alleviate optical aberrations and extend the depth of field of incoherent imaging systems whilst maintaining diffraction-limited resolution. It is particularly useful in controlling thermally induced defocus aberrations in infrared imaging systems. These improvements in performance are subject to a range of constraints including the difficulty in manufacturing an asymmetrical phase mask and significant noise amplification in the digitally restored image. We describe the relation between the optical path difference (OPD) introduced by the phase mask and the magnitude of noise amplification in the restored image. In particular there is a trade between the increased tolerance to optical aberrations and reduced signal-to-noise ratio in the recovered image. We present numerical and experimental studies based of noise amplification with the specific consideration of a simple refractive infrared imaging system operated in an ambient temperature varying from 0°C to +50 C. These results are used to delineate the design and application envelope for which infrared imaging can benefit from wavefront coding.