Hearts on Sunday beat Dundee United 2-1 to move up to sixth in the Clydesdale Bank Premier League, taking a place in the top half of the table for the first time since September.
With matches against Ross County on December 29 and Hibernian on January 3 to come before the winter break, McGowan hopes Hearts can consolidate their position towards the top of the table.
But he knows Killie, for whom Cillian Sheridan scored a hat-trick in a 3-1 win at Tynecastle earlier in the season, are a challenging proposition.
McGowan said: "It's an important time of year. Four games in quick succession is a huge challenge for us to get up the table where we should be.
"They've been good this season. They've got a great striker in Sheridan, who is scoring them goals.
"On paper we're a match for anyone and if we turn up and play in the right frame of mind, I'm sure we can get the three points."
McGowan, the younger brother of Australia international and Hearts right-back Ryan, made his third start of the season against United and performed well.
He was returning from injury and is confident of continuing in the side.
He added: "I've just got to keep on top of it. It's not 100% yet. It's just a little stomach tear. It's easy to play through, just as long as it doesn't happen again."