Real-time urban climate monitoring provides useful information that can be utilized to help urban management personnel to monitor and adapt their precautionary measures to extreme events, including urban heatwaves. Fortunately, recently created social media platforms, such as Twitter, furnish real-time and high-resolution spatial information that may be useful for climate condition estimation. The objective of this paper was to utilize geotagged tweets (participatory sensing data) for urban temperature analysis. We first detected tweets related to heat (heat-tweets). Then, we examined the relationships between monitored temperatures and heat-tweets through a statistical model framework based on copula modeling methods. We demonstrate that there are strong relationships between heat-tweets and temperatures recorded at an intra-urban scale, which are revealed by our analysis of Tokyo city and its suburbs. Subsequently, we investigated the application of heat-tweets for informing spatiotemporal Gaussian process interpolation of temperatures as an application example of heat-tweets. We utilized a combination of spatially sparse weather monitoring sensor data, which comprise infrequently available moderate resolution imaging spectroradiometer remote sensing data and spatially and temporally dense lower quality geotagged Twitter data. A spatial best linear unbiased estimation technique was applied. The results suggest that tweets provide the useful auxiliary information for urban climate assessment.