The symmetry of the room-temperature (RT) structure of title compounds La2-xSrxCoTiO6-delta changes with x, from P2(1)/n (0 <= x <= 0.2) to Pnma (0.3 <= x <= 0.5) and to R (3) over barc (0.6 <= x <= 1). For x = 1 the three pseudocubic cell parameters become very close suggesting a transition to a cubic structure for higher Sr contents. Similar phase transitions were expected to occur on heating, paralleling the effect of internal pressure induced by substitution of La3+ by Sr2+. However, only some of these aforementioned transitions have been thermally induced. The symmetry-adapted modes formalism is used in the structural refinements and fitting of neutron diffraction data recorded from RT to 1273 K. Thus, for x = 1, the out-of -phase tilting of the BO6 octahedra vanishes progressively on heating, and a cubic structure with Pm (3) over barm symmetry is found at 1073 K. For lower Sr contents this transition is predicted to occur far above the temperature limit of common experimental setups. The analysis of the evolution of the perovskite tolerance factor, t-factor, with both Sr content and temperature indicates that temperature has a limited ability to release structural stress and thus to enable transitions to more symmetric phases. This is particularly true when compared to the effect of internal pressure induced by substitution of La by Sr. The existence of phase transitions in materials for solid oxide fuel cells that are usually exposed to heating cooling cycles may have a detrimental effect. This work suggests strategies to stabilize the high-symmetry high temperature phase of perovskite oxides through internal-pressure chemically induced.