First, I'd like you to get the 'credentials' of your Termite Inspector. FWIW, recommending a fan to 'vent' an unheated crawlspace is inviting MORE trouble. AND, it's an invitation for the Termite Inspector to come back!
You see, the crawlspace is cool to begin with. When you add a fan that either pushes WARM air in (or draw COOL air out), the WARM air from the OUTSIDE that replaces the COOL air INSIDE will CONDENSE on the COOL surfaces in the crawlspace. Hence, you've just hastened the growth of mold and mildew, and all other types of problems, like TERMITES. In short, DON'T DO IT!
IF your crawlspace is dirt, be sure that your vapor barrier (on the ground) is at least 6 mil in thickness where you lay it on the dirt and overlap it about 6". Then, duct tape the pieces together. THEN, lay some 'weights' at interval on the edges (like bricks or Pressure Treated wood, or something.) This way, any moisture that 'rises up' into the crawl won't get past your vapor barrier.
IF, on the other hand, you have a poured crawlspace, OR a dirt one with water that's leaking into it other than from the ground, you need to 'collect it' and get rid of it. Per your assurances that your gutters and downspouts and sloping around the house are in good working order, you can build a pit and install a sump pump. Then, have it pump the water far AWAY from the house so it doesn't run back into the crawlspace.
It is to your BEST advantage to consider a foundation drainage system. (But where's the water coming from, and whence does it come??!) If you know the source, then THAT'S how I'd approach the solution. Maybe you DON'T need a foundation drainage system. Just don't put any fans in the crawlspace! If you haven't put on a raincoat and boots and carried an umbrella with you to inspect the ENTIRE perimeter of the house during a rain storm, I'd do so (when there's no lightening.) This will certainly assure you that your gutters, downspout, and foundation sloping are 'working' correctly.
Others may have more to say. My best to ya and hope this helps.