1994 Dodge Spirit charging system

In response to my prior message I did have my charging system checked, I was told I needed an alternator. However when starting my car after it sat overnight my battery voltage is back to normal. How can my alternator need replacing if my battery is recharged in the morning. Only when driving after the first four miles or so does my battery voltage drop to between 8 &10 volts on my guage. This only happens when my car engine tempature drops to normal. Thank you john young.