<p>The heat exchange between structural components and the environment occurred in the long-stroke CNC machine tools will cause non-negligible thermal deformation. The jumps and periodical components of ambient temperature have significant different impacts on the thermal errors. This paper introduces a novel add-on modeling method for long-stroke CNC machine tools considering ambient temperature jumps. This method employs multiscale wavelet decomposition to separate jump components from ambient temperature. Key innovations of the proposed method include as follows: (1) deriving differential equations for a single jump in ambient temperature based on the lumped parameter method and heat exchange principles, leading to the construction of a mathematical model for multiple ambient temperature jumps; (2) extracting the jumps component of ambient temperature using multiscale wavelet decomposition with the dB2 wavelet basis function; (3) constructing a periodic component model of ambient temperature using Fourier series decomposition; and (4) based on the separation method, a separation add-on modeling was proposed to increase the accuracy and robustness of exiting thermal error models. The proposed add-on method was validated in a long-stroke machining center in a large workshop environment. Experimental results demonstrate that, in comparison to 3 thermal error modeling methods (LASSO, CFNN, BPNN) without separating add-on model, the proposed model reduced maximum deviation more than 15% in the <i>X</i>-axis.</p>