Referenceless, or self-reference, thermometry is a technique for mapping temperature differences in the region of interest (ROI) using the baseline phase estimated by extrapolating the field in the surrounding region for estimation (RFE) and subtracting the estimated baseline from the measured field. In the present work a self-reference technique based on complex field estimation using 2D polynomials comprising complex-valued coefficients was proposed and optimized. Numerical simulations with a Gaussian-profiled phase distribution demonstrated that the ROI radius had to be 2.3-2.5 times the standard deviation (SD) of the Gaussian function in order to keep the error below 8% of the peak phase change. The area ratio between the ROI and the RFE had to be larger than 2.0 to maintain the error level. Based on the simulations, and phantom and volunteer experiments, the complex-based method with independently optimized polynomial orders for the two spatial dimensions was compared with the phase-based method using the similar-order optimization strategy. The complex-based method appeared to be useful when phase unwrapping was not removed. Otherwise, the phase-based method yielded equivalent results with less polynomial orders.