variavel0=Anai Lurdes De Boni - deboni@mksnet.com.br UNIJUÍ Viktor Georgievich Krioukov - kriukov@main.unijui.tche.br UNIJUÍ Luiz Carlos Martinelli Jr - martinel@main.unijui.tche.br UNIJUÍ Abstract. This work has aim to develop the mathematical model of a heat exchanger non-stationary "Air + Soil ". This heat exchanger intends to use of the subsoil temperature (that is almost constant during of year) to maintain the convenient temperature inside of building with small energy expenses. The heat exchanger yield depends on several factors: diameter and length of tube; thermal conductivity, specific heat and density of soil; time work. The developed mathematical model considers: air tube flow with the attrition and heat transfer, soil heat diffusion (with variation of the thermal conductivity), air temperature evolution of the heat exchanger exit. This model consists of a EDO`s and EDP`s system. The numeric simulations show the possibility to change the air temperature until DT = 10ºC during 10 hours with insignificant hydraulic losses. Keywords. Energy improvement, heat transfer, air, soil, mathematical modeling.