This is a β-hydroxyacid, but why doesn't it get dehydrated to give an α,β-unsaturated acid on heating?
The mechanism which I think should occur is:
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In order to obtain an α-β-unsaturated carbon acid from a β-hydroxy acid, you need a secondary or tertiary carbon in α 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 α-position leads to the olefin.
If you do not have that α-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.