By default fastcgi cache is stored in this location
/var/run/nginx-cache
which is mounted on tmps file system /run and it usually has around 10% allocated size. How much RAM does your server has? 10% is setup for a reason so if you don't have enough RAM increasing /tmpfs may not be a good idea. Anyway, you can check yours this way:
df -h and look for /run mount point. Depending on your server OS you can edit /etc/fstab file
sudo nano /etc/fstab
look for line similar to this:
tmpfs /run tmpfs noexec,nosuid,size=10%,mode=0755 0 0
edit size part to allocate more space, then close Ctrl-X and save. Then run:
mount -o remount /run and check to see if /run now has more size allocated to it.
Meanwhile, if you need to automatically clear NGINX/FASTCGI cache every day, you can add this to your crontab:
sudo crontab -e
and add the following line to it:
0 0 * * * ee clean --fastcgi