The photothermoelectric (PTE) effect uses nonuniform absorption of light to produce a voltage via the Seebeck effect and is of interest for optical sensing and solar-to-electric energy conversion. However, the utility of PTE devices reported to date has been limited by the need to use a tightly focused laser spot to achieve the required, nonuniform illumination and by their dependence upon the Seebeck coefficients of the constituent materials, which exhibit limited tunability and, generally, low values. Here, we use InAs/InP heterostructure nanowires to overcome these limitations: first, we use naturally occurring absorption "hot spots" at wave mode maxima within the nanowire to achieve sharp boundaries between heated and unheated subwavelength regions of high and low absorption, allowing us to use global illumination; second, we employ carrier energy-filtering heterostructures to achieve a high Seebeck coefficient that is tunable by heterostructure design. Using these methods, we demonstrate PTE voltages of hundreds of millivolts at room temperature from a globally illuminated nanowire device. Furthermore, we find PTE currents and voltages that change polarity as a function of the wavelength of illumination due to spatial shifting of subwavelength absorption hot spots. These results indicate the feasibility of designing new types of PTE-based photodetectors, photothermoelectrics, and hot-carrier solar cells using nanowires.