The remarkable accessibility of modern flying robots makes them an attractive platform for environmental sensing. However, low cost and ease of use are currently incompatible with large payloads, severely limiting the choice of sensor and ultimately modality. This paper describes the design of a system for using a small infrared thermometer to estimate the surface temperature over an area that is large compared to the area measured by the sensor, by mounting it on a flying robot. We leverage a priori knowledge about the spatial statistics of the phenomena under measure in order to plan an informative sampling path, fusing observations by Gaussian process regression. Our approach is designed to be evaluated in an indoor testbed, in which a quadrotor, in cooperation with simulated static sensing nodes, estimates the spatial distribution of surface temperature over a controlled thermal gradient. We perform extensive systematic experimentation both in simulation and our real-world testbed environment, with our algorithm estimating surface temperature to an accuracy of up to 2.1 °C over a 16 m2 area ranging in value from 25-65 °C.