We report on-off pointed MAMBO observations at 1.2 mm of 61 Spitzer-selected star-forming galaxies from the Spitzer Wide Area Infrared Extragalactic Legacy survey (SWIRE). The sources are selected on the basis of bright 24 μm fluxes (f 24 μm > 0.4 mJy) and of stellar dominated near-infrared spectral energy distributions in order to favor z ~ 2 starburst galaxies. The average 1.2 mm flux for the whole sample is 1.5 ± 0.2 mJy. Our analysis focuses on 29 sources in the Lockman Hole field where the average 1.2 mm flux (1.9 ± 0.3 mJy) is higher than in other fields (1.1 ± 0.2 mJy). The analysis of the multiwavelength spectral energy distributions indicates that these sources are starburst galaxies with far-infrared luminosities from 1012 to 1013.3 L sun, and stellar masses of ~0.2-6 × 1011 M sun. Compared to submillimeter selected galaxies (SMGs), the SWIRE-MAMBO sources are among those with the largest 24 μm/1.2 mm flux ratios. The origin of such large ratios is investigated by comparing the average mid-infrared spectra and the stacked far-infrared spectral energy distributions of the SWIRE-MAMBO sources and of SMGs. The mid-infrared spectra, available for a handful of sources, exhibit strong polycyclic aromatic hydrocarbon (PAH) features, and a warm dust continuum. The warm dust continuum contributes ~34% of the mid-infrared emission, and is likely associated with an AGN component. This contribution is consistent with what is found in SMGs. The large 24 μm/1.2 mm flux ratios are thus not due to AGN emission, but rather to enhanced PAH emission compared to SMGs. The analysis of the stacked far-infrared fluxes yields warmer dust temperatures than typically observed in SMGs. Our selection favors warm ultraluminous infrared sources at high-z, a class of objects that is rarely found in SMG samples. Indeed SMGs are not common among bright 24 μm sources (e.g., only about 20% of SMGs have f 24 μm > 0.4 mJy). Our sample is the largest Spitzer-selected sample detected at millimeter wavelengths currently available.