Parabolic wavelet transforms associated with the singular heat operators $-{\Delta }_{\gamma }+\partial /\partial t$ and $I-{\Delta }_{\gamma }+\partial /\partial t$, where ${\Delta }_{\gamma }={\sum }_{k=1}^n\partial ²/\partial x{²}_k+(2\gamma /xₙ)\partial /\partial xₙ$, are introduced. These transforms are defined in terms of the relevant generalized translation operator. An analogue of the Calderón reproducing formula is established. New inversion formulas are obtained for generalized parabolic potentials representing negative powers of the singular heat operators.