Why doesn't this β-hydroxycarboxylic acid undergo dehydration upon heating?
In order to obtain an &alpha;-&beta;-unsaturated carbon acid from a &beta;-hydroxy acid, you need a secondary or tertiary carbon in &alpha; position, because otherwise you would have to break a carbon-carbon bond, which requires a lot more energy then simply heating.

The mechanism is basically self catalysed, which is why this may happen easily with a little bit of heat. The acid may protonate intramolecular (or intermolecular) the hydroxy group. You have water as a nice leaving group, creating a carbocation, and abstraction of a proton in &alpha;-position leads to the olefin.

If you do not have that &alpha;-hydrogen, you are stuck with the carbocation. You might be able to obtain a lactone,like Waylander suggests, but I doubt this would easily happen with a little bit of heating, as spiro-compounds with four-membered rings tend to be quite unstable.



In your attempt you choose the less acidic hydrogen to transfer and then break a carbon-carbon bond resulting in a very unstable molecule which would rearrange to cyclohexanecarboxylic acid. I'd suspect you would need insane temperatures to overcome the activation barrier.