You can use [mg]awk:
awk 'NR==1{
header=$0;
count=1;
print header > "x_" count;
next
}
!( (NR-1) % 100){
count++;
print header > "x_" count;
}
{
print $0 > "x_" count
}' file
100 is the number of lines of each slice.
It doesn't require temp files and can be put on a single line.