Not likely. Read the package specifications here: Intel® Core™ i5-4400E Processor (3M Cache, up to 3.30 GHz) Specifications
Is it still working?
Have you checked for proper air flow?
Are the fans working?
Is the heat sink blocked with dust?
This message was posted on behalf of Intel Corporation
Thank you very much to Al Hill for the comments provided previously.
Besides trying the suggestions above, I just wanted to let you know that we do have a tool to test the processor, it does an overall test on it including a temperature test, if the processor passed the test it should be fine, second option to the left to install it:
Any questions, please let me know.