Single engine pilot reported high EGT during climb from a tower controlled airport in hot weather. The aircraft returned to the departure airport and landed safely.

Narrative

On a hot sunny day (97F outside) with an almost quick-turned airplane; right after take-off; we found out the EGT temperature was a lot higher than normal. We had already briefed about the hot temperature operation so immediately started the cruise climb. But the EGT started to keep rising to 1700 degrees; decided to call the Maintenance department about the issue. They have told us might be a sensor issue; but for safety; we decided to return to ZZZ. Cylinder 2 EGT kept rising to 2;000 degrees; decided to pull back more power to keep the engine cool. Had to fly downwind with 80 kts with 1900 RPM. After landing; EGT started to decrease rapidly; on parking it was 1300 degrees. Throughout the flight other cylinders 1;3;4 were in normal condition. There was no G1000 indication or warning about high EGT temperature. (Picture was taken after parking)Might be an actual sensor issue; but it was an extremely high temperature with a high-density altitude day. For an airplane almost did a quick turn might be not enough time for the engine to cool down. Fortunately; we found out early and decided to come back before further issues.High temperature always be cautious with your engine temperature. As emailed to CFI a couple of weeks ago about Aircraft X.