Equi-atomic FeRh is highly unusual in that it undergoes a first order meta-magnetic phase transition from an antiferromagnet to a ferromagnet above room temperature (Tr ≈ 370 K). This behavior opens new possibilities for creating multifunctional magnetic and spintronic devices which can utilise both thermal and applied field energy to change state and functionalise composites. A key requirement in realising multifunctional devices is the need to understand and control the properties of FeRh in the extreme thin film limit (tFeRh < 10 nm) where interfaces are crucial. Here we determine the properties of FeRh films in the thickness range 2.5-10 nm grown directly on MgO substrates. Our magnetometry and structural measurements show that a perpendicular strain field exists in these thin films which results in an increase in the phase transition temperature as thickness is reduced. Modelling using a spin dynamics approach supports the experimental observations demonstrating the critical role of the atomic layers close to the MgO interface.