This paper reports the thermal conductivity k of matched pair cell lines: two pairs of a normal and a cancer cell, one pair of a primary and metastatic cell. The 3ω method with a nanoscale thermal sensor was used to measure k at the single-cell level. To observe the difference in k between normal and cancer cells, the measurements were conducted for Hs 578Bst/Hs 578 T (human breast cells) and TE 353.Sk/TE 354.T (human skin cells). Then k of WM-115/WM-266-4, a primary and metastatic pair of human skin cell, was measured to find the effect of disease progression on k. The measured k data for normal and disease cell samples show statistically meaningful differences. In all cases, k decreased as the disease progressed. This work shows that thermal-analysis schemes, such as the 3ω method, have a potential to detect diseases at the cell level.