Additive manufacturing (AM) techniques can be applied to produce carbon-fiber-reinforced polymer (CFRP) elements. Such elements can be exposed to different environmental factors, e.g., temperature, moisture, and UV radiation, related to their operational conditions. From a variety of environmental factors, the temperature is one of the most typical. Temperature strongly influences matrix material joining together CFRP components, resulting in material strength reduction. Therefore, it is important to understand processes in the composite material caused by temperature. This experimental work investigated the thermal effects on the performances of AM CFRP composites. Specimens with unidirectional (UD) alignments of the fiber reinforcement were printed using the fused deposition modeling (FDM) technique. The printed specimens were subjected to two different thermal conditions: stable continuous at 65 °C and cyclic temperature between 50 and 70 °C. Tensile testing was performed to study the mechanical strength and Young’s modulus of AM UD-CFRPs. In order to investigate the morphological structure on the surface of AM specimens, an optical microscope, scanning electron microscope (SEM), and digital microscope were utilized. Untreated (intact) samples attained the highest average tensile strength value of 226.14 MPa and Young’s modulus of 28.65 GPa. The ultimate tensile strength of the sample group subjected to stable heat treatment decreased to 217.99 MPa, while the thermal cycling group reduced to 204.41 MPa. The Young’s modulus of the sample group subjected to stable thermal exposure was decreased to 25.39 GPa, while for the thermal cycling group, it was reduced to 20.75 GPa. The visual investigations revealed that the intact or untreated specimen group exhibited lateral damage in top failure mode (LAT), the thermally stable group underwent edge delamination in the middle (DGM) as the nominated failure mode, and the explosive breakage at gauge in the middle (XGM) failure mode occurred in the sample from the thermal cycling group. Based on morphological observations at the microscale, the delamination, fiber pull-out, and matrix cracking were the dominant damages in the 3D-printed tensile-tested specimens. The molecular chains of the polymer changed their structure into an amorphous one, and only local motions of stretching occurred when the specimens were exposed to stable heating (prolonged). In the case of thermal cycling, the strain gradients were accumulated in the matrix material, and the local stresses increased as a result of the reheating and re-cooling exposure of the polymeric composites; the molecular motion of the long-range polymer structure was reactivated several times. Micro-cracking occurred as a result of internal stresses, which led to material failure and a reduction of the mechanical properties.