We report on--off pointed MAMBO observations at 1.2 mm of 61 Spitzer-selected star-forming galaxies from the SWIRE survey. The sources are selected on the basis of bright 24um fluxes (f_24um>0.4mJy) and of stellar dominated near-infrared spectral energy distributions in order to favor z~2 starburst galaxies. The average 1.2mm 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 1.2mm flux (1.9+/-0.3 mJy) is higher than in other fields (1.1+/-0.2 mJy). The analysis of the sources multi-wavelength spectral energy distributions indicates that they are starburst galaxies with far-infrared luminosities ~10^12-10^13.3 Lsun, and stellar masses of ~0.2-6 x10^11 M_sun. Compared to sub-millimeter selected galaxies (SMGs), the SWIRE-MAMBO sources are among those with the largest 24um/millimeter 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 exhibit strong PAH features, and a warm dust continuum. The warm dust continuum contributes to ~34% of the mid-infrared emission, and is likely associated with an AGN component. This constribution is consistent with what is found in SMGs. The large 24um/1.2mm 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 ultra-luminous infrared sources at high-z, a class of objects that is rarely found in SMG samples. Our sample is the largest Spitzer-selected sample detected at millimeter wavelengths currently available.