"cross one's mind" and "enter one's mind"

The two verbs 'to cross' an 'to enter' are the key here:

v.tr.
1. To go or extend across; pass from one side of to the other: crossed the room to greet us

(Free Dictionary)

The connotations of cross are to go in and then out of, in your case, one's mind. Compare this to enter:

v.tr.
1. To come or go into: The train entered the tunnel.

(Free Dictionary)

Enter simply denotes the going in to one's mind and has no such connotation of it being fleeting.

Overall, the difference in verb choice makes crossing one's mind into just a brief thought - it comes and then goes - whethers enter, just means that a thought has gone into your mind but not out again.