If you can graduate with a bio-engineering degree, good grades, and do well on the MCAT, the undergrad institution shouldn’t impact your admission to Med school.
FWIW - Temple’s department is Bio-engineering, not bio-med. There are subsets in the department that allow for a more specialized focus, but it’s going to be different than the standard bio-med. They have a particular focus for pre-med, which I assume is what you’ve looked at/considered.
I don’t know what USC offers.