According to news reports, Timothy McVeigh, a lapsed Catholic, received the anointing of the sick, a Catholic sacrament, just minutes before his execution. snip
If this is the case, and McVeigh's confession and contrition were sincere, he received Christ's pardon for all his sins, thus reopening the way to heaven.
According to Catholic teaching, McVeigh faced his Lord and Savior for judgment immediately after his death. If he was indeed in a state of grace, he would be received into heaven or sent to an intermediate state called purgatory for a period of purification. There also he would be punished for past sins that, although repented, still needed to be atoned for.
What has become of the immortal soul of Timothy McVeigh? Only God knows. But if McVeigh confessed his sins, he did what the church required to have the merits of Christ's redemption applied to him. There the case rests.