It is a solid 15 hour drive one way between Mexico City and Chichen Itza. And a boring drive or bus ride at that. So that's not really practical with only a week in Mexico City.

If you insist on visiting Chichen Itza from Mexico City, given your time frame, I'd suggest flying to Merida and overnighting there or near the Chichen Itza site (which is approximately 90 minutes driving time from Medida). Get up early the next morning to enter the site when it opens, thus beating the bus tours and avoiding the afternoon heat and summer afternoon thunderstorms. Fly back to Mexico City in the afternoon or evening after your site visit.

Keep in mind that there is a fantastic archeological site (with two famous pyramids) outside Mexico City at Teotihuacan. Very easy to reach on your own or guided tour from Mexico City.

Summer is the rainy season in Mexico City (and the rest of Mexico in the tropical latitudes). Expect afternoon and evening thunderstorms with occasional downpours. In my experience it usually starts pouring right around rush hour, just adding to the misery of Mexico City's traffic.