Altermagnets present a class of fully compensated collinear magnetic order, where the two sublattices are not related merely by time-reversal combined with lattice translation or inversion, but require an additional lattice rotation. This distinctive symmetry leads to a characteristic splitting of the magnon bands; however, the splitting is only partial—residual degeneracies persist along certain lines in the Brillouin zone as a consequence of the underlying altermagnetic rotation. We consider a two-dimensional d-wave altermagnetic spin model on the checkerboard lattice and introduce additional interactions such as an external magnetic field and Dzyaloshinskii-Moriya interactions that lift these degeneracies. The resulting magnon bands become fully gapped and acquire nontrivial topology, characterized by nonzero Chern numbers. We demonstrate the crucial role of altermagnetism for the generation of the Berry curvature. As a direct consequence of the topological magnons, we find finite thermal Hall conductivity κ_xy, which exhibits a characteristic low-temperature scaling, κ_xy ∝ T⁴. Moreover, κ_xy changes signs under reversal of the magnetic field, exhibiting a sharp jump across zero field at low temperatures. We also demonstrate topologically protected chiral edge modes in a finite strip geometry.