Going "small scale" does not solve the heat problem unfortunately. If it does then the authors did not mention it. All they mentioned is how large scale plants deal with the problem.
Small-scale compressed air energy storage systems with high air pressures turn the inefficiency of compression and expansion into an advantage. While large-scale AA-CAES aims to recover the heat of compression with the aim of maximizing electricity production, these small-scale systems take advantage of the temperature differences to allow trigeneration of electrical, heating and cooling power.