This work reports a multispectral tomography technique in transmission mode (called 3DITI for 3D Infrared Thermospectroscopic Imaging) based on a middle wavelength infrared (MWIR) focal plane array. This technique relies on an MWIR camera (1.5 to 5.5 μm) used in combination with a multispectral IR monochromator (400 nm to 20 μm), and a sample mounted on a rotary stage for the measurement of its transmittance at several angular positions. Based on the projections expressed in terms of a sinogram, spatial three-dimensional (3D) cubes (proper emission and absorptivity) are reconstructed using a back-projection method based on inverse Radon transform. As a validation case, IR absorptivity tomography of a reflective metallic screw is performed within a very short time, i.e., shorter than 1 min, to monitor 72 angular positions of the sample. Then, the absorptivity and proper emission tomographies of a butane-propane-air burner flame and microfluidic perfluoroalkoxy (PFA) tubing filled with water and ethanol are obtained. These unique data evidence that 3D thermo-chemical information in complex semi-transparent media can be obtained using the proposed 3DITI method. Moreover, this measurement technique presents new problems in the acquisition, storage and processing of big data. In fact, the quantity of reconstructed data can reach several TB (a tomographic sample cube of 1.5 × 1.5 × 3 cm3 is composed of more than 1 million pixels per wavelength).