An innovative bioclimatic metric based on the Universal Thermal Climate Index (UTCI) is developed to quantify human thermal physiological heat stress. The Heat Stress Exposure (HSE) metric includes both duration and intensity dimensions of heat exposure, and in this paper it is applied to the Sydney Australia climatology. Geographic Information Systems (GIS) were used to spatially represent and visualize Sydney's HSE. The first stage of the analysis collated observed meteorological data from 10 weather stations across the Sydney metropolitan region, extending from coastal Sydney to approximately 50 km inland in 2017. The second stage of the analysis integrated the radiative meteorological data into estimates of hourly Mean Radiant Temperature which were then applied to UTCI. In the final stage, a threshold UTCI value of 26 degrees C was selected for the calculation of HSE, which was then cumulated to represent the duration of heat exposure throughout the year. The difference between each UTCI hourly reading and the 26 degrees C threshold defined a UTCI exceedance (Delta UTCI; degrees C). The cumulative total of all Delta UTCI throughout the year defined n-ary sumation Delta UTCI in units of degree hours (degrees C.hr), thereby capturing both intensity and duration of exposure to heat stress. Weather systems driving westerly winds from the Australian continent's central deserts brought the highest HSE to Sydney's inland western suburbs, with values ranging between 4,000-6,000 n-ary sumation Delta UTCI (degrees C.hr). Coastal eastern Sydney experienced considerably lower HSE values ranging from 1,600-3,000 n-ary sumation Delta UTCI (degrees C.hr), reflecting the moderating influences of sea breezes and evaporative cooling.