The characteristics of polycrystalline BaTiO3 metal-insulator-metal capacitors, fabricated using pulsed laser deposition, are investigated from room temperature to 420 K. The capacitance–voltage characteristics show ferroelectric behaviour at room temperature, with a phase transition to paraelectric at higher temperature. However, the permittivity response shows paraelectric behaviour across all measured temperatures. So BaTiO3 exists here in a mixture of cubic and tetragonal phases. The BaTiO3 films have a columnar structure, with grain size increasing with film thickness due to their increasing height but not diameter. This correlates with an increase in remnant polarization. The results support a size driven phase transition in thin films of polycrystalline BaTiO3.