A mathematical model is developed for calculating the temperature of the soil and air in a soil heat exchanger for ventilation systems. The model is based on the representation of temperature in the form of the Fourier integral. For high-frequency components with characteristic times of the order of 24 h an exact analytical solution is used. Calculation of low-frequency components with characteristic times of the order of a year is based on simulation of a tube by a linear heat source. The degree of decrease in the efficiency of the heat exchanger with decrease in the spacing between its tubes is evaluated. The dependences of the thermal power of the system on the length and diameter of the tubes, depth of their burial and air flow rate are calculated. An analytical expression is obtained for the optimum length of the tube. The evolution of the thermal power of the system during its operation for 10 years only in the winter period is calculated. The results of calculations are compared with experimental data. The procedure developed does not require cumbersome calculations and can be used for working out design recommendations.