{He that searcheth} (ho eraun(936e)). God ( 1Sa 16:7 ).
{According to the will of God} (kata theon). See  2Co 7:9-11 
for this phrase kata theon (according to God). The Holy Spirit
is the "other Paraclete" ( Joh 14:16 ) who pleads God's cause
with us as Christ is our Paraclete with the Father ( 1Jo 2:1 ).
But more is true as here, for the Holy Spirit interprets our
prayers to God and "makes intercession for us in accord with
God's will."