If you're careful not to heat the wort too quickly, you should be ok. If you heat it up too fast some parts of it might get hot enough to denature the enzymes you'll need to convert the rest of the mash. What you are proposing is similar in theory to decoction mashing, where a portion of the grain is removed and boiled, then added to the full mash to raise the temperature. What you are thinking of as far as getting the grains hot are tannins, and the problem tends to be more with high pH plus high temperature. With the buffering capacity of the wort, high temp isn't enough to draw tannins out, but once you get a really thin wort (like when steeping grains, or when fly sparging below 1.010), then tannins become more of a problem.
The other option is to start with a thicker mash with a low water to grain ratio (1qt/lb) and add boiling water to get get your temps up to where you're trying to go. Starting with a thick mash allows you to keep the mash in a decent range after adding the boiling water.
Finally, since it sounds like these are some of your first batches, have you considered skipping the protein rest? With the modification levels of modern grains, there isn't a biochemical need to do a protein rest, and it can even reach the point of being detrimental, removing some of the proteins you'll need for head retention. Often times, for a basic recipe, a single infusion mash at a moderate sacc temp (152-154) will work for most beers, then you can play with that temp for altering attenuation (146-158). Of course, some people like to do a protein rest to do decoctions (which are supposed to increase maltiness/mouthfeel) or just because its the original method for brewing, but if those aren't your desires, thought I'd try to save you some time!