After restarting a failed engine the pilot of a BE-36 returned to the departure airport.

Narrative

My clearance was initially to climb runway heading and to an altitude of 2000 MSL. After being handed off to Approach they cleared me to give best rate to 4000 MSL. I initiated the Vy climb when about 2200 to 2500 feet the engine briefly lost power. I leveled off to best glide and performed my air-restart emergency checklist. After the checklist was completed; the engine regained power and I requested a turn back to the departure airport for landing.Approach granted my request and cleared me to make a left downwind for Runway 15. Approach and Tower asked if I needed assistance and I declined both due to the engine's recovery. The reason I am writing the report is during the restart procedure; I may have deviated from the original clearance of runway heading and climb to 4;000 ft. The way I could have corrected the possible deviation is more awareness to spatial orientation and to react more slowly; not rush through situations such as an engine failure to prevent a deviation from the original clearance.