1. A non-transitory computer-readable recording medium in which a thermal fluid simulation program that carries out a simulation of a velocity field and a temperature field is stored, the program instructing a computer to execute: carrying out a first simulation of the velocity field and the temperature field of fluid flow, using a velocity-field analyzing model and a temperature-field analyzing model having respective first degrees of freedom; determining levels of reducing the first degrees of freedom based on a result of the first simulation; calculating a velocity-field dimension transformation matrix that reduces the degrees of freedom of the velocity-field analyzing model to second degrees of freedom of the velocity field by the levels of reducing determined; calculating, separately from the calculating the velocity-field dimension transformation matrix, a temperature-field dimension transformation matrix that reduces the temperature-field analyzing model to second degrees of freedom of the temperature field by the levels of reducing determined; converting the velocity-field analyzing model and the temperature-field analyzing model into reduced degree-of-freedom models having the second degrees of freedom using the velocity-field dimension transformation matrix and the temperature-field dimension transformation matrix calculated; and carrying out a second simulation of the velocity field and the temperature field of fluid flow using the reduced degree-of-freedom models, wherein the program further instructing the computer to execute: if a modification of an analysis condition is performed at a full dimension position previously designated in a full dimension space having the first degrees of freedom during the second simulation in a reduced analysis degree-of-freedom space having the second degrees of freedom under the analysis condition, before carrying out the second simulation in the reduced analysis degree-of-freedom space, calculating, based on the full dimension position and one of the velocity-field dimension transformation matrix and the temperature-field dimension transformation matrix, an operator that executes, in the reduced analysis degree-of-freedom space, processing related to the modification of the analysis condition at the full dimension position; and carrying out the processing related to the modifying of the analysis condition in the reduced analysis degree-of-freedom space using the operator calculated, wherein the operator includes: an adding operator that adds a setting value to the full dimension position, wherein the processing related to the modification of the analysis condition is carried out by adding the setting value to the full dimension position using the adding operator in the reduced analysis degree-of-freedom space; and a clearing operator that clears the state of the full dimension position to zero in the reduced analysis degree-of-freedom space, the program further instructs the computer to execute clearing the state of the full dimension position to zero using the clearing operator in the reduced analysis degree-of-freedom space, and adding the setting value to the full dimension position using the adding operator, wherein the processing related to the modification of the analysis condition is carried out by rewriting the state of the full dimension position to the setting value in the reduced analysis degree-of-freedom space.