Intramolecular Reaction with carbocation rearrangement
Your approach is feasible. Thermal cyclizations of appropriate dienes, enones, enynes, and other related unsaturated systems are known in literature. For example, there are extensive examples of intramolecular ene-reactions in Organic Synthesis and some of them are reviewed (Ref.1 and Ref.2). To justify your first step, I'd include the abstract of reference 1, which states that:


  Thermal cyclizations of appropriate dienes, enynes and related unsaturated systems, some of them carried out on an industrial scale, demonstrate increasingly the preparative power of the intramolecular ene reaction. A variety of substituted, fused and bridged ring systems, including natural products, are thus easily accessible in a regio‐ and stereo‐selective manner. Numerous examples are discussed systematically illustrating the possibilities, limitations, and common features of this cyclization reaction and its reverse ring‐opening process.


Nonetheless, see following example given in reference 1 for thermal cyclization:



Although those are different than the problem in hand, the intramolecular cyclization has possible clear path. For example, various types of intramolecular cyclizations has been discussed in Ref.1. Now, I modified your mechanism using arrows to make it clear:



The electrophile here is the carbonyl carbon of 1, which would get more electron deficient by carbonyl oxygen’s complexation to a Lewis acid such as $\ce{AlCl3}$, or  $\ce{AlEtCl2}$, or even $\ce{AlEt2Cl}$ (Ref.2). This is evident in the intermediate I. The neucleophile, the alkene group of the molecule is in close proximity to make a bond with elecrophilic carbonyl carbon (intermediate II). The driving force here is making a less strained 5-membered ring and relatively stable $3^\circ$-cabocation. Keep in mind that all of these intermediates are reversible. The reversible hydride transfer is possible because energy different between resulting $3^\circ$-cabocations are minimal. Yet, this transfer facilitate pinacol-pinacolone type rearrangement of methide shift to give final stable product 2.

References:


Wolfgang Oppolzer, Victor Snieckus, “Intramolecular Ene Reactions in Organic Synthesis,” Angew. Chem., Int. Ed. Engl. 1978, 17(7), 476-486 (https://doi.org/10.1002/anie.197804761).
Barry B. Snider, “Lewis-acid catalyzed ene reactions,” Acc. Chem. Res. 1980, 13(11), 426-432 (https://doi.org/10.1021/ar50155a007).