Induced thermal-lens spectroscopy with a common-path interferometer has been used for high-sensitivity measurements of green-light induced absorption dynamics in single-domain and periodically poled KTiOPO4. Although the linear infrared absorption in both materials is the same, the saturated green-light induced absorption is consistently higher in periodically poled crystals. Initial relaxation of the induced absorption is also different in these materials where periodically poled KTP does not exhibit as fast initial relaxation characteristic as the single domain KTP. These differences in the absorption are explained by higher concentration of native defects associated with weakly bonded K+ ions, which stabilize electron and hole traps forming color centers in the material. Unannealed as-poled crystals also exhibit characteristic overshoot dynamics in the induced thermal lens signal, which signifies remnant stress in the domain walls. Investigations showed that the lattice vibration energy generated by the dissociation of induced color centers is sufficient for complete relaxation of this remaining stress. The sensitivity of the measurement technique is demonstrated by the measurement of small signal absorption in the blue spectral region arising during continuous wave quasi-phase-matched second harmonic generation in periodically poled KTP.