It is very unlikely that you have a thatch problem this soon after a new lawn intallation. If you can post some pictures you may get an answer that may save you a lot of time and money. BTW a machine that dethatches is called a power rake--same thing. The process of making holes in the lawn is aeration and the machine is called an aerator. Plug aeration is the most recommended type.

I can assume you have a cool season grass if you are in zone 6. If the lawn is trampled (ie compacted), rent a coring aerator and over seed. Make numerous passes over the lawn to get a lot of holes. Helps to water the lawn to soften it up before you aerate. Fertlize with a starter fertilizer the same day you seed. Make sure you keep the soil moist (not soaked) for 7-10 days and you should be good to go.

Lawns, like other plants, go into dormancy---that's what protects them from harsh winters--and roots wont germinate new growth in such low temperatures. To put a greenhouse over a specific area, with conditions that would encourage such growth, wouldn't persevere long enough and any such germination wouldn't last very long once the conditions that encouraged such growth was removed. Remember...its the soil temperature---not any for a brief period that encourages growth. lasts. You just have to accept such conditions until spring--and the rebounding of soil temperatures which will hasten germination and growth.

The app rate for compost is 1 cubic yard per 1,000 square feet. The reason I say that is you did not mention it but you did mention several things that give me the impression you might jump off a cliff if someone suggests it. CGM is no guarantee you will not have weeds. I've used it many times as a fertilizer and it doesn't seem to stop any weeds for me. NONE. It's a hellofa fertilizer, though. Compost tends to make your lawn warm up earlier than the neighbors, so you might see improvement before they do. Compost is also the most expensive thing you can put on your lawn. I think you would get much more benefit from alfalfa or anything else. I'm guessing you have fescue and no Kentucky bluegrass. If you want to end your problems with thin turf, plant the best Kentucky bluegrass seed you can buy. The dense KBG should keep the weeds out permanently. On the down side, it turns brown in the winter. For that reason many people mix TTTF with KBG. They both have benefits.