This study proposes a method employing acoustic tomography for simultaneous measurement of temperature and gas velocity fields in furnace. Accounting for the refraction effects of sound waves, a multi-physics acoustic reconstruction model is established using a Radial Basis Function Neural Network (RBFNN). The process begins by developing enhanced RBFNN-based models tailored to reconstruct temperature and velocity fields along the propagation paths of sound waves. Subsequently, the model's parameters, including the distribution of reference points, RBF shape parameters, hidden layer neurons, learning rate, and the number of iterations, are optimized, with specific value ranges determined for each. Numerical simulations are then carried out on representative physical field models within the furnace, and the results are compared with traditional reconstruction algorithms such as Tikhonov Regularization and TSVD. The simulations demonstrate that the proposed method offers significant improvements in both collaborative reconstruction of 2D and 3D temperature and velocity fields, with better adaptability, stronger noise resistance, less consumed time and higher accuracy. Finally, field data of a high-temperature vortex flow in a boiler obtained from computational fluid dynamics model is carried out to prove the ability of the novel method. This collaborative multi-field measurement lays a foundation for further optimization of combustion processes within furnaces.