Well, let’s see.
To thaw a 1.5 metric ton colossal squid frozen in a block of ice (the only way the fishermen who trawled the thing in could bring it home before it went bad), scientists put it in a big vat of brine just above 0 Celsius/32F. That allowed the fresh water to melt while still keeping the squid as cold as possible. Essential, since for a giant corpse with tentacles, certain parts are bound to thaw days before others and could become quite rotten before the rest comes out of the ice block if you’re not careful.
HOWEVER Captain America was still alive, which complicates things. On the other hand, even supersoldiers are significantly smaller than this record-setting colossal squid. This helps thaw logistics somewhat.
Much like the squid, Captain America would have to be kept at a consistent temperature throughout his body in order to be thawed successfully. If his extremities were to thaw more than a minute or two before his heart and lungs were thawed and reactivated, the tissue wouldn’t have any oxygen and would quickly die. What a shame to bring back Steve Rogers only to have him be the poster boy for gangrene. Brain tissue becoming metabolically active before the cardiovascular system began functioning would be even more disastrous— possible permanent brain damage.
And the GH-325 project was born
To keep his temperature as equal as possible across his entire body, something like the squid brine or (more likely) an antifreeze solution would be used. Immerse the Capsicle in brine until the entire unit is within a degree or two of thawing* to begin Phase II.
*Note that due to presence of salts, fats, protein, etc, the freezing point of meat is actually 28-29F. Apologies to non-US readers, sadly I only work with American meat and don’t know the freezing point of corpses/beef in Sane Country Units. That being said, Steve Rogers is 100% American meat. Fahrenheit shall be considered the appropriate unit for this project.
At the thawing point, it’s important to consider life support functions. I don’t know how fast human tissue uses up oxygen at refrigerator-range temperatures, but I’m going to assume that the sooner you have oxygen circulating the better. A heart-lung machine would be needed to oxygenate and move the blood around for a while before the heart gets started back up.
Meanwhile, because Captain America’s last un-frozen moments were spent deep underwater, there may be decompression issues at play. Whatever gas bubbles may have been present in his tissue are currently frozen in place, but when he thaws they can move about and create embolisms —> the bends. Better put him in a hyperbaric chamber just in case.
Since Captain America regained consciousness in a recovery room rather than during the thaw process, it may be safe to assume that he was sedated and/or placed in a drug-induced coma during thaw.
So at this point we’ve got a giant bathtub of brine, a heart-lung machine, oxygen canisters, lots of drugs, plus all the necessary monitoring equipment all inside a hyperbaric chamber. After thawing the antifreeze bath could be replaced with gradually warming water or saline solution in order to bring Captain America back up to normal body temperature. So many machines! This is US medicine at its finest.
Forced warm air blowers (hairdryers) are needed after Captain America is fully thawed, organ systems are reactivated, and he is brought back to normal body temperature. At this point it becomes necessary to dry and style Captain America and put him in period-appropriate jammies to sleep it off in a vintage hospital room. If you think hearing the wrong baseball game tipped him off fast, you should see him wake up with bad hair.
