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This paper presents work on the analysis of the effect of Joule heating on sheet resistivity measurements using Greek cross test structures. As part of this work, design rules have been derived to minimize the heating effect associated with currents forced during their measurement. To accomplish this, finite-element (FE) simulations were employed to identify the location of heat generation and cooling mechanisms in the structures. This identified that the temperature could be minimized by: firstly, decreasing cross arm length, and therefore both electrical and thermal resistance of the arms; and secondly, by integrating pads and leads to improve the heat sink effect. These results were confirmed by sheet resistance measurements of four different Greek cross designs which demonstrated that the proposed design rules reduced the Joule heating effects on the sheet resistance measurements by up to 25%.