Welcome to th 7 Forum geralph.
I have no idea how you can loose 20 GB of hard drive space just by rebooting. I do know that Windows 7 needs a little working space on the hard drive to work properly.
When it sees that the space is limited it will give you warnings and that is good. Using my 3 brain cells of memory I'm thinking Windows likes about 10% of the hard drive for working room. Removing things off of the hard drive or installing a bigger hard drive is two ways of solving this problem. If it was my computer I would remove things from the hard drive. Take a read through this and you will find other things that can help. Optimize Windows 7
A infection can be using up your hard drive space without you knowing it unless you do some scans. Using a utorrant can also use hard drive space and get you infected.
I would do some scans with these before you move anything to another storage device. Moving things before the system is clean just infects the other storage device.
ESET Free Online Virus Scanner | ESET
Windows Defender Off Line Windows Defender Offline
To put things in order.
1. Scan your computer for infections when clean
2. Remove things from hard drive
3. Go through the Tutorial Optimize Windows 7.
--------------------------------------------- Please note:
If a infection is found all the things your have already transfered to the external storage will be infected also.