Altermagnets, a recently discovered class of magnets, uniquely merge the zero net magnetization of antiferromagnets with the spin splitting characteristic of ferromagnets. By harnessing the advantages of both---such as enabling anomalous transport without stray fields and supporting ultrafast spin dynamics---altermagnets offer exciting prospects for advancing dissipation-free spintronics and spin-caloritronics. In this study, we conduct detailed symmetry analysis and advanced first-principles calculations to investigate the intrinsic anomalous Hall, anomalous Nernst, and anomalous thermal Hall effects in the two-dimensional topological altermagnet ${\mathrm{V}}_{2}{\mathrm{Te}}_{2}\mathrm{O}$. In the nonrelativistic limit, monolayer ${\mathrm{V}}_{2}{\mathrm{Te}}_{2}\mathrm{O}$ exhibits $d$-wave spin splitting and hosts two spin-polarized nodal loops near the edge centers of the Brillouin zone. Upon incorporating spin-orbit coupling, the nonzero tensor elements of all three anomalous transport conductivities are identified using magnetic group theory. Depending on the orientation of the N\'eel vector, the nodal loops become partially or fully gapped. The curvature of the nodal loops significantly enhances the anomalous Nernst conductivity at room temperature while maintaining the validity of the anomalous Wiedemann-Franz law up to 200 K. These findings position ${\mathrm{V}}_{2}{\mathrm{Te}}_{2}\mathrm{O}$ as a compelling two-dimensional altermagnetic platform for exploring the interplay between altermagnetism, topological nodal structures, and anomalous transport properties, paving the way for advancements in altermagnetic spintronics and spin-caloritronics.