I cannot test it, but this should work:
Data = load('FileName.MAT', '-MAT');
If this can import files with any extension assuming they have MAT format, why shouldn't this work for '.MAT' also?
Anyway, I'd prefer a clean naming scheme instead. But I had some '.MAT' files also on an old ISO9660 CD, such that renaming would require a copy to the hard disk at first.