Different from second-order temporal ghost imaging usually realized by means of second-order correlation measurement, in this paper, we investigate theoretically temporal imaging with temporally thermal light via first-order field correlation based on a Mach-Zehnder interferometer. The paraxial wave equation describing the diffraction of light and the differential equation characterizing the dispersion of light pulse are given. Based on the similarity between these equations, the duality between the paraxial diffraction of the light in the spatial domain and the dispersion of the temporal narrow-band pulse in the dispersive medium (i.e. the space-time duality) is obtained, and the impulse response functions in the time domain for several optical systems are also presented. Then in terms of the space-time duality, we design the scheme for temporal imaging via first-order thermal field correlation based on a Mach-Zehnder interferometer and obtain the intensity expression for first-order temporal imaging according to the temporal impulse response functions, and discuss the influences of the source pulse width and coherence time on the image visibility and resolution. The result shows that the temporal signal can be reconstructed through temporal first-order temporal imaging. Furthermore, when the source’s coherence time is fixed, the image visibility decreases as the pulse width increases. However, the image resolution increases. When the source’s pulse width is fixed, the image visibility increases as the coherence time increases. And yet the image resolution decreases. Specially, when the source’s pulse width is 100 ps and the coherence time is 0.5 ps, the image quality (taking both the visibility and resolution into account) of a temporally rectangular object is satisfactory. In the simulation, the distance and width of the temporal rectangular object are 20 ps and 8 ps, respectively. It is shown that there is a dilemma between the visibility and resolution of first-order temporal imaging which is similar to the result of second-order ghost imaging. Our result discussed herein could be valuable in the reconstruction and detection of temporal signal via first-order temporal ghost imaging with temporally thermal light.