in efi engine electrical fuel pumps prime the rail at click of key. to prime fuel rail, click key 3 times in 15 seconds then crank engine with throttle slightly pressed.
the symptoms are of dirty fuel filter pouch inside the pump assembly and the purge valve. both items are service parts and can be purchased new from parts market.
engine start is hardly any effect over cold engine in any case thermostat valve is closed or open. Engine performance does have serious impact after engine warm up and system going in loop if thermostat valve is missing.