A many-body potential for strontium clusters is developed with parameters fitted to the energy surface of strontium clusters containing up to ten atoms calculated within the density functional theory in the generalized gradient approximation. Structure and energetics of the most stable cluster isomers with up to 63 atoms are obtained with genetic algorithms. Additionally, the high resolution mass spectrum of strontium clusters up to Sr-96 at finite temperature is provided. Several thermodynamic properties are studied under the many-body potential as a function of temperature. It is found that stability patterns, indicating how stable a cluster size is with respect to its neighboring sizes, change significantly with temperature. This behavior is due to structural transitions of the strontium clusters that occur at finite temperatures. A comparison with the experimental mass abundance indicates that only the structures above 400 K were observed experimentally. Very prominent magic numbers are predicted at 34 and 61.