Abstract This paper deals with the problem of an infinite cylindrical heat source embedded into a saturated porous medium and subject to a cross-axial Darcian flow. Only forced convection is considered. We derived the transient dimensionless solution through a combined analytical – numerical method consisting of four steps: (a) a preliminary dimensional analysis of the constitutive equations of the problem in order to find the dimensionless groups governing the solution; (b) the identification of the validity range of the model as a function of the just-mentioned dimensionless groups; (c) the numerical resolution of the problem; (d) the synthesis of the numerical results in a general dimensionless form. Specifically, we provide several dimensionless maps of the 2D thermal field evolution for six different orders of magnitude of the Peclet number ( 10 - 3 – 10 2 ) . The evolution of the temperature of the heat source is fully illustrated and discussed through plain dimensionless criteria. Then, we discuss the time, space and fluid velocity scales in which the solution is practically equivalent to the ones given by a linear heat source and a purely conductive model. We conclude that the present model has to be employed to evaluate the temperature in proximity of the heat source when the reference Peclet number is greater than 0.5. On the contrary, the linear model can be successfully used for radial distances 5–10 times greater that the heat source radius, depending on the reference Peclet number.