The mechanism of heat transfer intensification recently brought about by nanofluids is analyzed in this article, in the light of the non-Fourier dual-phase-lagging heat conduction model. The physical problem involves an annular geometry filled with a nanofluid, such as typically used for measurements of the thermal conductivity with Blackwell's line heat source probe. The mathematical formulation for this problem is analytically solved with the classical integral transform technique, thus providing benchmark results for the temperature predicted with the dual-phase-lagging model. Different test cases are examined in this work, involving nanofluids and probe sizes of practical interest. The effects of the relaxation times on the temperature at the surface of the probe are also examined. The results obtained with the dual-phase-lagging model are critically compared to those obtained with the classical parabolic model, showing that the increase in the thermal conductivity of nanofluids measured with the line heat source probe cannot be attributed to hyperbolic effects.