In any wavelength sensitive application, extensive care should be taken in addressing the wavelength drift issues. In the case that laser tuning is conducted by using thermoelectric cooler, an accurate expression is needed to describe transient characteristics of Peltier device to achieve maximum controllability. In addition, thermal tuning issues are of particular relevance to the field of photonic integration. In this study, the exact solution of the governing equation is presented considering Joule heating, heat conduction, heat flux of laser diode and thermoelectric effect in one dimension. In addition, variable separation method and Sturm-Liouville theorem, along with the completeness features of eigenfunctions, are used to obtain time-dependent electrical potential and temperature distribution of the Peltier device. Additionally, steady state sensitivity analysis is performed in order to demonstrate the impacts of physical parameters on its thermoelectric characteristics. Transient temperature is also considered which, for a specific case, revealed fast transition to steady state condition with time constant lower than 400 ms. Lower heat capacity as well as laser diode heat flux might lead to faster Peltier response times, such that the effect of heat flux on response time becomes negligible in low heat capacity Peltier.