The CPU in the Pro 3 models are different than the models used in the Pro 2. Even though they are "Haswell" chips, they are built completely different and are not the same type that can be installed in a desktop or laptop (which the Pro and Pro 2 did use).
They are flatter in design and wider to actually increase cooling capability (at least, designed to do so) and that may not be the case.
The temperature sensor settings are most likely different as well (as you may have noticed) and in fact, the Surface Pro 3 tablets are first time the i3, i5, and i7 processors are being used in. So, that means there is no track record of actual performance.
Do make sure you do not block the vent holes that surround the perimeter of the Pro 3.
Also, power management has not been a "grand" feature in Surface tablets (all of them) and I have the RT and shut it off completely for both battery and A/C. I have absolutely no problem out of that machine after I did that and you may need to do something
similar with yours. Go manual on your power management settings and attempt to set a power plan that will work better. It may reduce some of the problems you are encountering and like I said, there is no track record for these particular processors and you
will just have to feel your way around and experiment.
The i5 is quite capable of running high end games but in a tablet, the CPU will not be the problem, it will be the lightweight components it has to work with. That would apply with any tablet.
Just not robust like a laptop even though that is how the Surface models are being used.