This article describes a method to determine geothermal gradients and formation temperatures using bottom-hole temperatures (BHTs) from wireline-log headers and then tests the method by applying it to analyses from more traditional sources. Bottom-hole temperatures, depths, and times since circulation ended were collected from at least one well in every township that had been drilled for petroleum exploration in the state of Wyoming. Using approximately 3500 BHTs collected from almost 2000 wells, equations were developed for average formation temperatures and geothermal gradients across the state. A method of correcting the average data to true formation temperatures in each individual well was also developed. The geothermal temperatures so derived very closely match temperatures from production BHTs that are the normal industry standard for formation temperatures and suggest that BHT information is much more accurate than commonly thought. The use of BHT measurements to compute temperature gradients was also developed. The effects upon formation temperatures of common data recording errors; of vertical circulation of groundwater, especially above 1700-m (5577-ft) depth; and of lateral groundwater circulation through deep aquifers are documented. The methods developed offer promising avenues for research in the areas of hydrogeology, geothermal exploration, determining formation temperatures, and heat flow.