I left a frozen wet cured fully cooked ham still in the shrink wrap in a cool water circulation last night to thaw it. At some point my wife used the faucet and set the temp on the tap up. When I reached in to pull the drain, the water was warm and so was the ham. It had been in this warm state for no more than 3 hours. I shot a temp on the exterior of the ham and it read 100.2F. I immediately put it back in the frig to wait till the morning to cook. Will it be safe to consume after reaching 160?
Wet cured ham spoilage
ham
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This is really an issue of risk.
The USDA's recommendation is not to consume meat that has experienced more than four hours of cumulative time between 40° and 140° F. Essentially, that means that the level of risk of illness from food-borne pathogens is acceptable in that range. The government's position is that 5 hours beyond a level of risk that they are willing to expose the public to.
Also be aware that (sliced) deli meat is more prone to pathogens that a whole ham.
That said, it comes down to what level of risk you are comfortable with. Personally, I would probably eat it myself, but not serve it to others.
If it is a country ham, meaning salt-cured then you need to boil the salt out of it. I may get flamed for this, but that article is not how I process my ham. So here is what I do.
I get a lard tin, I usually have to cut off the hock to make the ham fit but since yours is split you may not have to. If it is not a salt cured ham, and is a city ham it may not be fit to eat if you do this, you could make ham soup maybe.
Anyway put the ham in the tin fill it full of water bring it up to a boil let it boil for about fifteen minutes then bring the heat down to medium-low for about 1/2 an hour then let it cool down enough so you can take it off the stove, but just barely cool enough. While it is cooling down get blankets and spread them out on the floor, one or two thin ones should do, then get some newspaper and spread that in the middle of the blankets put the tin in the middle of the newspaper and wrap the tin with the newspaper then wrap the blankets around it and then push it over into a corner overnight.
The next morning pull the ham out of the water give it a rinse and pat it dry, it will still be warm-to-hot. (I rotisserie ham hocks and small hams I get from my butcher but I have never done a full size ham I would imagine the amount of drippings would make a mess though.) Next I get my big roasting pan put the ham in it and pat it down with brown sugar, medium or dark is up to you. Then I cover it with aluminum foil, making sure I tent the foil so it doesn't touch the ham, and let it cook usually between four and five hours for a good size ham at about 325. The last half hour I take off the aluminum foil and if I feel it is necessary I add more brown sugar and let it caramelize.
I have been cooking ham this way for as long as I have been cooking and the process is passed down from my mother and her father before her. Farther back than that I cannot confirm or deny. :)
Here is a great article on country hams and other hams, just to make sure you do have a country ham, and gives other great suggestions on how to cook a ham, although they do it differently than I do.
http://www.amazingribs.com/recipes/porknography/zen_of_ham.html
Best Answer
I am usually loath to say out loud that you can feel safe going outside of government guidelines, even if I wouldn't hesitate to eat the food myself. In this rare case I will throw caution to the wind. Oh for heaven's sake, cured ham? Warm for <3 hours? Yes, you can eat it.
I can't swear that it is actually safe, but you're probably more likely to be struck by lightning than to be made sick by that ham (unless by some weird twist of fate, it was tainted to begin with).
The official USDA line is that 40F - 140F is the "danger zone", and any food that is susceptible to becoming dangerous is dangerous if it has spent more than 2 hours (cumulative, as in ever) in that temperature zone. That is obviously very, very conservative. Curing adds another layer of preservation/safety to the meat.The USDA would say that your ham needs to be thrown out. I say pass the mustard.
If any member of your family is pregnant or immunocompromised, give them actual "safe" food.