Thermal adaptation of organisms is a property emerging from the complex interplay of biophysical constraints and selective forces. The shape of thermal performance curves has been well investigated but we lack knowledge of how they may evolve. Two extreme cases can be expected: i) under the hypothesis of local adaptation, species should shift their thermal performance curves and have an optimum at the temperature at which they evolve, or ii) under the hypothesis of thermodynamical constraints, universal biophysical rules dictate a fixed performance curve with an optimum at warm temperatures. We perform an evolutionary experiment to test these two hypotheses on the thermal response of bacteria growth rate, expecting a strong evolutionary response of the thermal performance curve. We use four wild bacterial strains and allow them to evolve at ten different temperatures (ranging from 8.5 to 40°C) to subsequently measure their growth rate at these ten temperatures. We investigate the difference in growth rate between evolved lines and their ancestors. We observe signs of adaptation, as growth rates of evolved and ancestral strains exhibit small but significant differences. Our analysis shows however that the shape of the thermal performance curves does not systematically vary between evolved and ancestral strains, and none of the evolved lines have an optimal growth rate at the evolution temperature. One strain grows significantly faster than its ancestor at the temperature of evolution, but we find that for other strains, evolution leads to faster as well as slower growth rates. These differences are repeated between evolutionary replicates, suggesting they are selected. Our study demonstrates that adaptation does not always overcome thermodynamical constraints on growth rates, and helps to better understand how microbes will respond to temperature changes.