What could be causing cold water to enter my hot water tank?
If water is flowing back through the hot line with the shut off valve closed on the cold (inlet)line would indicate a leak in the tank or a faulty shut-off valve not completely closing. If the supply valve is off (closed) water flow stops. Check for air in the tank by opening the pressure+ relief valve with the cold valve shut. Water should sputter from it (hot! be careful) or air, initially and than water.    Also, if possible, check for a H+C pipe reversal along the out going tank line. Primary locations to check would be the fixtures you are opening to increase the hot water temperature.