Cold atmospheric plasmas (CAPs) are increasingly used for treatment of complex surfaces in biomedical and biomaterials processing applications. However, the multivariable, distributed-parameter, and nonlinear nature of CAP dynamics and plasma–surface interactions, coupled with the sensitivity of plasmas to exogenous disturbances, make their safe, reproducible and effective operation challenging. This paper adopts a data-driven linear parameter-varying (LPV) modeling framework to learn a control-oriented model for predictive control of a kHz-excited atmospheric pressure plasma jet in Helium. A hierarchical model-based control strategy is proposed based on a supervisory LPV-based model predictive controller (LPV–MPC) to regulate the nonlinear thermal effects of plasma on a surface. Real-time control experiments demonstrate the effectiveness of the proposed LPV–MPC strategy for the multivariable control of surface temperature and plasma optical intensity, as well as for controlling the spatial delivery of the cumulative thermal effects of the plasma jet on a surface.