There is a renewed interest in MR-guided laser interstitial thermal therapy (LITT) as a minimally invasive alternative to craniotomy for local treatment of various brain tumors and epilepsy. LITT allows for focused delivery of laser energy monitored in real time by MRI, for precise ablation of the lesion. Although highly promising, the long-term effects of laser ablation as a viable treatment option for neurological disorders have yet to be rigorously studied and quantified. In this work, we present a quantitative framework for monitoring per-voxel thermal-induced changes post-LITT over time on multi parametric MRI. We demonstrate that voxel-by-voxel quantification of MRI markers over time can enable a careful and accurate (a) characterization of early LITT-related changes (if and when they are exaggerated and when they subside), and (b) identification and monitoring of MRI markers that potentially allow for better quantification of response to LITT therapy. The framework was evaluated on two distinct cohorts of patients (GBM, epilepsy), who were monitored post-LITT at regular time-intervals via multi-parametric MRI. On a cohort of six GBM studies we found that (a) it may be important for the initial treatment-related changes to subside to more reliably capture MRI markers relating to tumor recurrence, and (b) T1w MRI and T2-GRE may better differentiate changes that may correspond to tumor recurrence from patients with no recurrence, as compared to T2w-MRI, and FLAIR. Similarly, our preliminary analysis of four epilepsy studies suggests that (a) early LITT changes (attributed to swelling, edema) appear to subside within 4-weeks post-LITT, and (b) ADC may be more reflective of early treatment changes (up to 1 month), while T1w may be more reflective of early delayed treatment changes (1 month, 3 months), while T2-w and T2-FLAIR appeared to be more sensitive to late treatment related changes (6-months post-LITT) compared to the other MRI protocols under evaluation.