Do T-cells express MHC molecules?
There are two types of MHC molecules:

All nucleated cells express MHC class 1 proteins.  A sample of all proteins produced within the cell are 'sliced' into their constituents which are then presented by MHC-I receptors.  This means that if a virus infects a cell, the foreign proteins the cell is induced to make are expressed on the cell membrane by MHC-I.  This is important as antibodies can not cross cell membranes, therefore this is the method by which a cell signals that it is infected by a virus.  

MHC II are the special molecules that are only expressed in antigen-presenting cells, which I think is what you are referring to.  As neither CD4 or CD8 T-cells present antigens, they do not express MHC-II themselves.  Instead CD4 have receptors for MHCII  (while CD8 have receptors for MHCI), allowing them to interact with antigens presented by other immune cells.  

If a virus infects T-cells, the viral proteins are sampled by the MHC-I pathway and presented via MHC-I on the surface of the infected T-Cell.  The immune response then progresses as for any other virally infected cell, destruction by CD8 T-Killers that destroy the cell by non-phagocytic means.