An inverse solution technique utilizing the conjugate gradient method of minimization and the adjoint equation is used to estimate the initial condition for a one-dimensional heat conduction problem in a plate, with no prior information for the functional form of the spatial variation of the initial condition. Simulated experimental data is generated by adding random errors to the calculated exact temperatures at the sensors locations. Two different types of experiments considered included: (i) the sensors are located at the boundaries and temperature measurements are taken at different times, and (ii) The sensors are placed at different locations in the medium and temperature at each sensor is measured at a specified time.