It depends on how you would like to tackle the problem. Another approach could be to try to estimate the probability of failure within the next X periods.
Models that are associated with these kind of problems are based on survival analysis and the most common models are the Kaplan Meier estimator (https://en.wikipedia.org/wiki/Kaplan%E2%80%93Meier_estimator) and Cox-Regression (https://en.wikipedia.org/wiki/Proportional_hazards_model). You can easily find existing packages in python and R.
Apart from the Holt Winter's model, you could also use Prophet. (https://github.com/facebook/prophet). The good thing about prophet is that it analyses the time series for you, so potential trend or seasonality can be obtained immediately.
Consider also to apply a feature extraction method where you split time into periods and build features like minimum Temperature, max, mean, correlation measures etc. Then based on these periods you could use any kind of ML algorithm to predict either the remaining useful time or probability of failure within the next X periods.
I would also propose to you to study literature on this topic (https://en.wikipedia.org/wiki/Prognostics). There are many different available approaches tackling real-world problems.
Finally you could check other datasets (https://ti.arc.nasa.gov/tech/dash/groups/pcoe/prognostic-data-repository/) that are associated with these kind of problems and try to exercise on multivariate analysis.
I hope this helps.
EDIT: I forgot to mention ARIMA model. It is basically a linear regression based model but it is a possible alternative that you could consider.