Response time correction and smoothing of time-series temperature data

I have some time series data of skin temperature measurements from human subjects. These subjects underwent a series of temperature transitions. However, the devices used to measure skin temperature had a slow response time. I'd like to do a rough correction of these measurements based on some response time data I collected retrospectively. I have a very crude correction matrix based on the difference in temperature measurements over time between a quick response device and the slow response device used. This can be used as the basis of the correction. I've also attached some example graphs showing the type of correction I'm referring to.  In addition, I'd also like to smooth the data to remove minor fluctuations, and interpolate from 5 second intervals down to 1s intervals using a public spline interpolation. The aim of the correction exercise is to correct the general trend of skin temperature change following the transition. There is data from 13 subjects, each with 13 skin temperature measurements. There are 6 transitions in total. Data will be provided as an Excel file (.xlsx). The corrected and smoothed data should be returned in the same document upon completion. The data file and any addition details will be given to the successful applicant. Desired Skills MATLAB, Data Science, Data Analytics, Data Cleansing, Mathematica