TL;DR = Coconut oil increases metabolism in the sense that it doesn't require your body to perform any additional work to metabolize the energy in the oil. Does it increase your metabolic efficiency overall? No. In fact, greater weight-loss is evident with Long-Chain Triglycerides than with Medium-Chain Triglycerides.
My emphasis in bold below...
Medium chain fatty acids found in coconut oil are absorbed by the GI tract (gastrointestinal) with ease. They do not require any pancreatic enzymes to break them down, which means less work for your pancreas. Next, medium chain fatty acids are shipped to the portal blood stream, directly to the liver, where they go directly into mitochondria without the use of the carnitine palmitoyl transferase, and are immediately oxidized for energy. MCFA (medium chain fatty acids) from coconut oil do not get packaged up with lipoproteins, and do not get transported to a variety of tissues and are not stored as body fat, they go directly to the liver and are metabolized for energy.
See: (Life Sciences 62 (14): 1203-1215)
In this article, medium chain fatty acids of 8-10 carbon long
increases activity of lipase and thus absorb to the intestine at a
much faster rate than long chain fatty acids. Study indicated that
medium chain fatty acids do not need a lipoprotein for transport but
can transport straight to the mitochondria via portal circulation for
beta-oxidation. In this paper, other oxidative process such as
omega-oxidation and peroxisomal-oxidation occurs in the liver. As seen
before, long chain fatty acid need some sort of transport to other
organ through the blood. Most often with long chain fatty acids, a
carnitine shuttle is required to get the fatty acid into the
mitochondria to do beta-oxdation. With medium chain fatty acids, a
shuttle is not needed. Energy intake and stored from medium chain
fatty acids metabolism is much more sufficient than long chain fatty
acids. Appoximately 13% more energy intake compare to long chain fatty
*acids* (Papamandjaris, Macdougall, Jones, p. 1209). We see than medium
chain fatty acids metabolism is more efficient in which the intake and
storing of energy is greater than that of long chain fatty acids.
Here is an abstract from another study involving rats:
Volume 14, Issue 1, February 1995, Pages 23–28
Protein and energy metabolism were examined in 34 partially
hepatectomized rats (70%), receiving total parenteral nutrition (TPN).
The TPN contained either long chain triglycerides (LCT) or
triglycerides comprising both medium- (MCFA) and long chain fatty
acids (LCFA) on the same carbon skeleton (MILT, medium- and long chain
triglyceride). The rats were divided into 4 groups with and without
glucose (G) supplementation: LCT+G, LCT-G, MLT+G, MLT-G. 3 days after
surgery protein synthetic rate in skeletal muscle, as evaluated from
in vitro incorporation of 14C-phenylalanine into muscle protein, was
significantly higher in rats receiving MLT if compared to rats
receiving LCT (p < 0.05). Rats receiving MLT lost significantly less
weight during the study period when compared to the LCT group (p <
0.005). Increased leucine oxidation was observed in rats receiving TPN without glucose regardless of the type of fat emulsion used (p <
0.05). In conclusion, when given to partially hepatectomized rats TPN containing both MCFA and LCFA exerts a stimulatory effect on muscle
protein synthesis and preserves body weight better than an emulsion
containing LCT only.
For other information concerning Lipids and Energy Storage/Useage, see this wikibooks link.