Thermal gradient is best tested by aiming the camera at a surface of uniform temperature and emissivity. A Black Body source is specified by manufacturers for such tests.
House walls can have a thermal gradient across their surface. A painted sheet of metal at room temperature would likely do for the tests that you are interested in however. Paint the metal sheet with matt black cellulose, acrylic or enamel paint from a spray can. Try to keep the paint thickness thin and even to avoid differences in the surface emissivity.
I have tested my E4 previously and it DOES have a thermal gradient at narrow spans. I am not concerned with such at the E4 price point though. From memory, early testing of the E4 showed that the transmission range from the outer to centre of the E4 lens had to be compensated for in the calibration tables, and an area at the centre of the camera image did display a gradient compared to the periphery of the image. Such gradients only become apparent when working at narrow spans however and are not of concern to many.
I should state that I do not consider the E4 to be a truly radiometric thermal camera as its accuracy as you move away from a target at 30C decreases. Accuracy at low temperatures close to 0C is appalling ! For the money, the E4 is great value and we have to forgive some of the compromises that had to be made to keep the BOM cost down, such as not using a Germanium lens. If I was the owner of a genuine, ex factory, E8, I might not be so forgiving however !
Aurora