We use Spitzer MIPS data from the FIDEL Legacy Project in the extended Groth strip to analyze the stellar mass assembly of massive (M>1011 Msolar) galaxies at z<2 as a function of structural parameters. We find 24 μm emission for more than 85% of the massive galaxies morphologically classified as disks, and for more than 57% of the massive systems morphologically classified as spheroids at any redshift, with about 8% of sources harboring a bright X-ray- and/or infrared-emitting AGN. More noticeably, ~60% of all compact massive galaxies at z=1-2 are detected at 24 μm, even when rest-frame optical colors reveal that they are dead and evolving passively. For spheroid-like galaxies at a given stellar mass, the sizes of MIPS nondetections are smaller by a factor of ~1.2 in comparison with IR-bright sources. We find that disklike massive galaxies present specific SFRs ranging from 0.04 to 0.2 Gyr-1 at z<1 (SFRs ranging from 1 to 10 Msolar yr-1), typically a factor of 3-6 higher than massive spheroid-like objects in the same redshift range. At z>1, and more pronouncedly at z>1.3, the median specific SFRs of the disks and spheroids detected by MIPS are very similar, ranging from 0.1 to 1 Gyr-1 (SFR=10-200 Msolar yr-1). We estimate that massive spheroid-like galaxies may have doubled (at the most) their stellar mass from star-forming events at z<2: less than 20% mass increase at 1.7