Hyundai Repair: intermittant engine response, ambient air temperature, sonata 4

Question
The TSB was brought to the attention of the service mgr who claimed it had been complied with, but that the computer did not indicate a 'change' when they were finished.  In addition, the event occurred one time with the car cold-soaked to an ambient temp of 50F.  As the temps cooled off the last couple of weeks, the starter cranked ever slower until this morning the car would not start.  The charging system is fine, and I replaced the battery.  Could a weak battery have been causing all of this?
Gordon
-------------------------------------------
The text above is a follow-up to ...

-----Question-----
2003 Sonata 4 cyl: Sometimes right after start, the engine will not accelerate when the gas pedal is pressed.  Works ok when hot or cold but not if engine is between 80 and 120 deg F.  It idles fine, and if left idling for 60 seconds or so it accelerates normally.  The warranty is up in 250 miles, and it has been to the dealer twice in the last month.  They can't find anything wrong.
Thanks
-----Answer-----
There's a reprogram available for this condition.  Perhaps you should bring Hyundai TSB 05-36-006 to their attention.  According to the TSB, the reprogram addresses "reduced power and/or hesitates under the following conditions:
• The ambient air temperature is high (above approximately 80°F).
• The ambient humidity is high (above approximately 50%).
• The condition lasts for approximately 30 seconds to one minute after start-up.
• The engine is cold with the coolant temperature close to the ambient air temperature."  
It also states "vehicle has no other driveability related conditions" and "vehicle runs as expected after approximately 30 seconds to one minute."

If you'd like to view the TSB in it's entirety-- I cannot provide it here due to copyright protection-- you can do so at www.hmaservice.com.  You'll need to register for a free account, and the site requires Internet Explorer.  This particular TSB is in .pdf format.

Answer
Although I agree it sounds like you have a weak battery, I doubt that has anything to do with actual engine performance once the engine is started.

I'm confused about the statement about computer not indicating a change.  When the tool is hooked up and instructed to reprogram, it should either read "already reprogrammed" or it should do the reprogram.  If neither of these things occurs, it doesn't sound like the procedure was followed properly.  But I'm also in no position to say whether you have the current software in the computer.  The easiest way to check is to hook up the scan tool and read the version from the computer, and compare that to the table in the TSB, or just attempt to reprogram and see what message is returned.