Hi Meccathor and welcome!
I recently moved my tanks 5 miles to our new house. The process is basically the same, but I didn't really take any precautions with heat and aeration like you should.
First, get the fish into buckets with the old tank water. Don't fill the bucket up all the way to the top as the water will slosh in the car. Also, don't feed them that day or the day before, so they don't foul the bucket water. Some people have used insulated food carriers to retain some of the warmth of the water. Maybe someone else can share their experience on keeping the water somewhat warm. You may be able to use an aquarium heater plugged into the cigarette lighter. My drive was only about 10 minutes, so I just turned up the car heater. You can also find a battery-powered aeration device at your lfs to keep the water aerated to supply oxygen to the fish as you transport them. Pack the bucket/cooler in another box if necessary to keep it stable during the drive. You can also put your filter media (depending on how big it is) in a clean panty hose and in the buckets with the fish too.
I would empty all the water remaining in the tank and save some if it's feasible. I used empty gallon bottled-water jugs. This way, your fish will not be stressed by brand-new water parameters at the new house - you can mix some of their old water with the new water. If it's not feasible, don't worry about it - just do a thorough acclimation when you set the tank up. I saved about half the old water in the tank and filled the rest with new water at the new house.
The plants (if you want to keep any) will be fine in a paper towel dampened with tank water, and then put the paper towels in a baggie, fish bag, or zip-top plastic bag.
Depending on how big the tank is and how feasible it is for you, I found that it made my job easier just to throw away the substrate at the old house. I took the tank out to the yard (we had a warm day in December!) and squirted it clean. Then I put it in a garbage bag and put it in the car. At the new house, I put a new bag of substrate in. You can save the substrate in a baggie or garbage bag, but it will be stinky, and if you don't have a huge tank - maybe buying that much substrate again isn't feasible for you - then I think buying new substrate for the new set-up will be easier.
As you set up the tank, dechlorinate some of your new tap water and mix with your old water if you brought any. Fill the tank with this mixture and then run a drip line to the fish buckets to begin acclimating them. I like this acclimation kit:
http://www.drsfostersmith.com/product/prod_display.cfm?pcatid=16100&Nty=1&Ntx=mode+matchallpartial&Ntk=All&pc=1&N=0&Ntt=acclimation%20kit&Np=1 You could also put a heater in the fish bucket at this time. I left my fish in the bucket until the tank water and bucket water were equal. I used two heaters in the tank at set-up (removing one later) to get the water up to the right temperature.
Remember to check water parameters often after the tank is set up since you may go through a mini-cycle (some bacteria may have died during the transport, and if you got new substrate you've lost some bacteria). You may have to do a few extra water changes to keep things stable, but your remaining bacteria should quickly catch up.
If you did get new substrate, you'll probably go through the diatom phase again. I did, but I still would rather deal with the diatoms than try to save smelly substrate!
That's up to you, but don't leave the substrate in the tank for transporting if at all possible. The shifting weight of the substrate could crack the tank.
Good luck!
