Check your new cooler, remove it and repaste/reseat, see below:
Normal causes for MCE errors include overheating and/or incorrect hardware installation. Specific manually-induced causes include:
overclocking (which normally increases heat-output)
poorly-fitted heatsink/computer fans (the same problem can happen with excessive dust in the CPU fan)
an overloaded internal or external power-supply (fixable by upgrading)
Computer software can also cause MCE errors (normally by corrupting data which programs read or write). For example, software performing read or write operations from or to non-existent memory regions can lead to confusion for the processor and/or the system bus. Accessing memory marked off-limits by UEFI may cause MCE errors.