B737-700
Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 204
Time Pressure; Distraction
Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Weight And Balance
Flight Crew Returned To Departure Airport; Flight Crew Inflight Shutdown; General Declared Emergency; General Maintenance Action
Aircraft
On climbout the number one engine overheat illuminated. I was the PM. We complied with the QRH procedures and declared an emergency. I completed the checklist up until the One Engine Inoperative Landing Checklist and then transferred control; so that I could conduct the landing. In the rush I inadvertently calculated the landing weight incorrectly; which resulted in an overweight landing. I did not discover the error until after we landed and I talked to the Dispatcher. The actual landing weight was calculated by Dispatch as 128;300 pounds.I had calculated 125;300 pounds. Because of the proximity to the landing field; I only had time to notify Base Operation to relay to Dispatch of our situation and that we were returning to [departure airport.] Dispatch did not have time to contact us airborne to relay the landing data; which we had already calculated. The computation confusion came about as everything was very rushed while trying to complete the QRH procedures and prepare for landing in a very short amount of time. I discussed the issue with the Dispatcher and entered the overweight landing in the logbook. I also discussed the issue with Maintenance Control.
The engine overheated on climbout at about 200 feet to 300 feet. We referenced to the QRH and shut down the engine. We declared an emergency and returned to [departure airport.]
B737NG flight crew experienced a left engine overheat shortly after takeoff. They shut down the engine per QRH and declared an emergency.  A safe but modest overweight landing occurred due to an inadvertent miscalculation.