Wandering temperature gauge

Last July I purchased a 1988 BMW 325i convertible. When ambient temeperature began to fall the car began running cold. I then decided to change the thermostat and discovered that the one installed in the car had three 1/8" holes drilled in the frame. I assumed that the previous owner did not care to change the thermostat and looked for a cheap option in the summer time. With the new thermostat the car reaches the middle point in the gauge after about 5 minutes and many times stays there. Sometimes it will take of from there to about 3/4 and then suddenly jump to just bellow the red area, jumping back an forth in a split of a second. Then, after a while it will go back to 1/2 or just past it. Any hints? Thanks in advance.