We studied the kinetics of swelling in high-χ lamellar-forming poly(styrene)-block- poly(lactic acid) (PS-b-PLA) block copolymer (BCP) by varying the heating rate and monitoring the solvent vapour pressure and the substrate temperature in situ during solvo-thermal vapour annealing (STVA) in an oven, and analysing the resulting morphology. Our results demonstrate that there is not only a solvent vapour pressure threshold (120 kPa), but also that the rate of reaching this pressure threshold has a significant effect on the microphase separation and the resulting morphologies. To study the heating rate effect, identical films were annealed in a tetrahydrofuran (THF) vapour environment under three different ramp regimes, low (rT<1 °C/min), medium (2<rT<3 °C/min) and high (rT>4 °C/min), for 60, 90 and 120 min, respectively, while the solvent vapour pressure and the substrate temperature were measured in real time. The translational order improved significantly with increasing the heating rate. The solvent mass uptake calculated for the different ramp regimes during annealing is linearly proportional to time, indicating that the swelling kinetics followed Case II diffusion. Two stages of the swelling behaviour were observed: (i) diffusion at the initial stages of swelling and (ii) stress relaxation, controlled at later stages. Films with a faster rate of increase in vapour pressure (rP>2 kPa/min) reached the pressure threshold value at an early stage of the swelling and attained a good phase separation. According to our results, highly ordered patterns are only obtained when the volume fraction of the solvent exceeds the polymer volume fraction, i.e., (φs≥φp), during the swelling process, and below this threshold value (φs=0.5), the films did not obtain a good structural order, even at longer annealing times.