Is it feasible to use decision tree algorithms for sensor fault detection? The gist is me wanting to separate system faults from sensor faults given some dataset from a wireless sensor network using a machine learning algorithm. 

For instance, if I have some temperature sensors in a given area and their corresponding readings from every sort of time interval, I would like to know whether an abnormal value is due to an actual fault, or due to a faulty sensor. Of course, it would be a given that the training set would have such entries tagged with either sensor fault or system fault.

I have thought of just using something like linear regression but I would like it to work even if the system could not be modeled like that. Decision tree seemed to me like a more appropriate algorithm for this.

Lastly, there is also some consideration for the time it takes for training and classification as I wish to see if it can be used for systems which respond really quickly to such anomalies.

Sorry if it's a bit wordy but I wasn't sure how much information I should put since this is my first time posting (I'm not even sure if this is the right stack exchange to post this). Anyway, thanks in advance for the answers!
You need to determine how to formulate your problem. I see it as having two aspects:
1. Detect an abnormal value (in temperature)
2. Determine whether abnormal value is due to sensor or system problem

The first is an anomaly detection problem and there is lots of literature on the topic, including tree-based methods on sensor data. One prominent approach is Isolation Forests, which is implemented in scikit-learn. http://scikit-learn.org/stable/modules/generated/sklearn.ensemble.IsolationForest.html

The second is fault localization. This is an area also well described in literature, and tree-based models were used even before machine learning became a thing.
A key here is to only train on anomalous data, then this should become a relatively simple classification problem assuming your have relevant features.