Growth and magnetic characterization of thin films of Co2Cr0.6Fe0.4Al and Co2MnSi full-Heusler compounds are investigated. Thin films were deposited by magnetron sputtering at room temperature directly onto oxidized Si wafers. These Heusler films are magnetically very soft and ferromagnetic with Curie temperatures well above room temperature. Polycrystalline Co2Cr0.6Fe0.4Al Heusler films combined with MgO barriers and CoFe counter electrodes are structured to magnetic tunnel junctions and yield almost 50% magnetoresistance at room temperature. The magnetoresistance shows a strong bias dependence with the maximum occurring at a voltage drop well above 1V. This special feature is accompanied by only a moderate temperature dependence of the tunnel magnetoresistance.