It is highly unlikely that this file is EASILY recoverable by native Windows built-in tools based on it being deleted 2 minutes after you download it fully since it is getting deleted that soon right after the download completes.
If you have volume shadow services enabled or even backups to tape, unless those processes run right before the deletion occurs, it's highly unlikely you'll be able to easily recover these files from the hard drive.
You may be able to find a third party tool that can recover files written to the hard drive and then deleted but it may be just as simple to download the file again. Also, you need to be careful when installing a tool on the same hard drive you are going to recover from as it may write over the same space on the hard drive where you need it to recover from and cause further troubles.
Please note that I answered this question before I had 50 points to post a comment or I would have done this as a shorter comment maybe in that case. I also answered this hypothetical question before someone mentioned that questions should be practical and not hypothetical. I do also realize there are MANY FACTORS to consider with data recovery so this answer to the hypothetical question asked is brief and general based on home usage from a Windows PC that was deleted two minutes after it was saved to a temporary download location with some sort of FREE tool or software data recovery method.
Finding the cause of what's deleting this file may be best so check your AV software in case it's deleting it due to it being found to be malicious.