CRJ-900 Captain reported high temperatures and wake turbulence from a preceding A300 led the flight crew to miss an altitude restriction on the departure procedure.

Narrative

Climbing out of SDF on the GTGON Departure. We briefed the departure and crossings and noticed the GNZOH restriction above 12000. The airplane was accelerating about 280 kt. and when I noticed this I disconnected the autopilot and pitched up. We were right at or maybe below a couple hundred feet off this restriction. The outside air temp was 34°C and airplane was at 80k lb. at takeoff. We took off behind an A300 and I was in and out of his wake turbulence on takeoff as well.I should have climbed at a slower speed to make this restriction.