CRJ900 Captain reported a hard landing while attempting to compensate for gusty winds and turbulence.

Narrative

I possibly had a hard landing coming into ZZZ. I was Pilot Flying (PF) and the First Officer (FO) was Pilot Monitoring. We were coming into ZZZ and landing Runway XX; doing the ILS on a clear day with a 40 degree crosswind from the right. The wind was 260 at 11G18. The approach was fine; I noted that I was flying at the top of the speed bug to compensate for the wind gusts and the heat thermals from the ground that I was fighting to maintain a stabilized approach. The speed was fluctuating about +/- 5kts with constant light turbulence throughout the entire descent. During the last 100 feet I began to pull power back and slowly pitch up the aircraft to arrest the descent. At this time my FO called out 'REF +5' and I began to slightly pull the power back. I was looking down at the end of the runway during the flare and noticed that I hadn't quite flared as much as I'd like to. To avoid jamming the gear into the ground I didn't pull back any harder on the yoke and let the plane sit. But it wasn't until in the flare that I had realized with the gusts I needed to have had a little extra power just a little sooner and we hit the ground hard. I don't know the exact FPM we impacted but it was between 800-600fpm. I think in the end I might've cut the power too soon and didn't flare quite enough to arrest the full descent. I wrote up the incident and notified maintenance to ensure the aircraft was safe to continue and I also discussed with the flight attendant to ensure no passengers were harmed. There were no injuries or aircraft damage. A miscalculation of thrust and pitch required to arrest the descent and compensate for gusty wind conditions while landing. Continue to be proactive about correcting for airspeed and altitude throughout the landing process and even after touching down.