I do feel your pain. There's nothing like a nice hunk of meat. Technically you can cool it down in time if you are careful.
Small hunk, not a whole darn cow mind you.
HOME METHOD This only works in a Large Upright or Chest Freezer with enough empty space for good Air Circulation!...Even Small hunks of meat will raise the temp in the small Refrigerator Freezer to levels that can cause partial defrost and refreeze...While there can be some safety issues, the major issue is thaw and refreeze seriously Damages the Texture and Quality of the other items in the Freezer...
Let it rest. If you cooked in a pan, you must now transfer it from the hot pan into a cool pan,--aluminum foil one will work fine for this . Stick that sucker in the freezer (aluminum foil pan will allow you to bend it in and wedge that sucker in there) uncovered to cool down faster. DO NOT BAG IT and whatever you do DO NOT COVER IT. If it's in aluminum foil remove any foil wrappings. Check the inside temp in an hour. Your goal is to get it down to 70 degrees within 2 hours. This can be done in the freezer.
ROAD METHOD
If you are out on the road barbecuing , camping, with the folks, etc, this will be more difficult. (I don't recommend the hillbilly ice bath in cooler method but it can be done). In this case a half cooler filled with ice. Your beef chunk has rested and you have to bag it so it's cool enough that you can get a bag around it. Note: The entire top of the bag is open so the heat can vent. now you stick it down in the ice, leaving the top open and vented up.
EITHER WAY
Now keep in mind this is for a nice size hunk not something enormous. The food must cool in stages cooled from COOKED° to 70 ° within two hours and from 70 ° to 41 ° in the next four hours. You may think hey, I got six hours to do this this is easy right? Problem is its harder to cool from stage one to stage two wherein the bacteria grows and everyone is wondering why they have the craps the next day. Sure was yummy.
I don't like to recommend cooling hunks but try this and keep thermometer handy and you can do it. Thoroughly clean the Thermometer with Hot Soapy Water or with an Alcohol soaked wipe or Paper Towel between tests...