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Thank you for contacting the Intel® Communities.
As per the screenshots received, the temps are ok in your system.
I personally use the software on the right side to monitor my temps, it will change the color to orange or red when temps are going high.
The TCASE for your Intel® Xeon® Processor E5405 would be 67°C, any temps below that would be fine for your system.
Unfortunately, the CPU information for HP ProLiant ML150 is not available in the screenshot provided, but still the TCase can be checked by looking the model of the processor here: ARK | Your Source for Intel® Product Specifications> TCase under Package Specifications.
Regarding the temps that can be handled by the other components of your system, my recommendation would be to contact directly the manufacturer.
Tech specs for HP ProLiant DL380e Gen8 look for "temperature": http://www8.hp.com/h20195/v2/GetPDF.aspx/c04128166.pdf