@LightningZ71 is correct, the i7-7700T is the model that you would need.
What CPU do you currently have? The computer you listed has four different 35W i5 models (6500T, 6600T, 7500T, and 7600T). I'm asking since the i5-7600T and i7-7700T are not very different. If you already have the 7600T, then you might not be happy with your upgrade. You might get better performance just clearing the dust out of your mini computer and maybe putting on new thermal paste in that case. But, if you have the i5-6500T, then the performance boost will be noticeable. Not earth shattering, but noticeable.