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A supply container may be much bulkier for it's weight than bombs. While there maybe room in the fuselage (or not, depending on fuel tanks):
http://img35.imageshack.us/img35/2922/heinkelhe177a5greifarti.jpg
Getting any real amount of supplies though the existing hatches and passageways may have been a real problem.
Good transports have large volume in addition to good weight capacity. High performance bombers have small fuselages (small volume).
A supply container may be much bulkier for it's weight than bombs. While there maybe room in the fuselage (or not, depending on fuel tanks):
http://img35.imageshack.us/img35/2922/heinkelhe177a5greifarti.jpg
Getting any real amount of supplies though the existing hatches and passageways may have been a real problem.
The HE177 might not have been the best choice as a transport but it could have been usefull towing gliders.
I think cooling wasn't exactly the strongpoint of the db610.
"The airfield is easy to pin-point from 4,500 – 5,000 feet owing to its rolled runway, its wreckage and the numerous bomb craters and shell holes. The landing cross was covered with snow. Directly my machine came to a standstill the airfield was shot up by ten enemy fighters – which, however, did not come lower than 2,500 – 3,000 feet owing to the light flak that opened up on them. Simultaneously it was under artillery zone fire. I had just switched off the engines when my aircraft became an object for target practice. The whole airfield was commanded by both heavy and medium guns situated – so far as one could judge from the open firing positions – mainly to the south-west . . .
"Technically speaking, the airfield can be used for daylight landings, but at night only by thoroughly experienced aircrews. . . Altogether thirteen aircraft wrecks litter the field, in consequence of which the effective width of the landing area is reduced to eighty yards. Especially dangerous for night landings of heavily laden aircraft is the presence of the wreck of a Bf 109 at the end of it. Immediate clearance of these obstacles has been promised by Oberst Rosenfeld. The field is also strewn with numerous bomb canisters of provisions, none of them saved, and some already half covered with snow . . .
" When I returned to my aircraft (after reporting to General Oberst Paulus) I found that it had been severely damaged by artillery, and my flight mechanic had been killed. A second aircraft of my section stood off the runway in like condition. Though I had landed at 1100 hours, by 2000 hours no unloading team had appeared, and my aircraft had neither been unloaded nor de-fueled despite the crying need for fuel by the Stalingrad garrison. The excuse given was the artillery fire. At 1500 hours Russian nuisance planes (U-2s) began to keep watch on the airfield in sections of three or four. From the outset I made it my business to look into the air control system and established that before 2200 hours it was quite impossible to land a single plane. . . If one approached, the seven lamps of the flare path would be switched on, offering a target visible for miles, whereat it would be bombed by the nuisance raiders above. The only possible measure was a short flash to enable the aircraft to position its bomb canisters . . ."