Heating aliphatic carboxylic acids with glycerol (and optionally a catalytic amount of a strong mineral acid) will esterify the components to form various triglyceride esters. The procedure is called Fischer esterification. It will not happen at room temperature (>100°C is suitable) or in aqueous solution.
Neither "oil" or "butter" could be classified as "aliphatic carboxylic acids" though. Stearic acid could, however, and is the main constituent of top-grade old-style candles.
Here is a PPT presentation dealing with the esterification of Glycerol with Stearic Acid, forming Tristearin (a triglyceride ester):
http://www.chem.uic.edu/wardrop/teaching/chem234/files/WARDROP-234-17.ppt (http://www.chem.uic.edu/wardrop/teaching/chem234/files/WARDROP-234-17.ppt)
Both vegetabilic oils and animal fats come as triglyceride molecules: http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/F/Fats.html (http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/F/Fats.html)
Free fatty acids are relatively uncommon to find in large amounts in nature: http://en.wikipedia.org/wiki/Fat (http://en.wikipedia.org/wiki/Fat)