Darendor,
Oh my.
Battery: $100
Solar Charging System: $150
DC to AC Power Inverter: $70
$350
Control Unit: Find electronics student at RDC and offer $100 to design it...?
...where to start?
You had best save your $100 for the "student" and the $150 for the solar charging unit (For the record, $150 + $70 + $100 = $320, and if you add the $100 for the "student", you get $420).
Let's assume a 200W heating element, as that seems on the low side of "standard". 200W/12V = 16.7A. Let's assume the battery you are referring to is a standard 12V deep-cycle lead acid battery @ 105Ah capacity. 105Ah/2 = 52.5Ah/16.7A = 3.14 hours of operation.
Let's assume you can find a 36W solar charger for your $150; 36W/12V = 3A. 60Ah/3A = 20 Hours to recharge 52.5Ah battery @ 87.5% efficiency. So, it is safe to assume that a $150 solar charger is NOT going to keep your battery charged.
Why, if I stated your battery had a capacity of 105Ah, did I divide that figure by 2? If you drain a lead acid battery below ~50% capacity it shortens the life of the battery considerably. Granted, "deep cycle batteries" do better than "cranking batteries" wrt "deep discharge cycles", but in the climate you are discussing, if you expect your battery to last a year, draining it to more than 50% capacity should be avoided.
So, we can eliminate your $150 solar charger. If you need more than ~3 hours of heating @ a time, you should spend some of this "savings" on more batteries. You should charge your batteries via you vehicle's alternator. Assuming a 75A alternator, you should be able to charge one battery (3.5 hours of operation) per hour of vehicle run time.
Assuming you are not going to need the heater while the car is running, and assuming you have some notion of what the temperature is outside, instead of worrying about a temperature sensor with digital display, a power switch and some blinking lights, you might consider buying an inverter with a power switch already installed on it, and simply turning the switch on when you exit the vehicle and off when you return.
So far, you have only batteries and an inverter on your shopping list. If you add a cigarette lighter plug adapter with battery clips to your list (~$10.00), your system is almost complete! Your vehicle's charging system will keep your battery charged to the proper level w/o any auxiliary charging system as long as the usage time to drive time is maintained.
If your usage involves a 30 minute drive to work and 9 hours of parking with the heater on, you would need to add a battery charger to your shopping list, and attach it to your batteries @ night. To figure the charger size:
9 hours * 200W / .8 = 1.44kWh ==> 1.44kWh / 12V = 120Ah. 120Ah/52.5 = 2.28 batteries, round up to 3 batteries to ensure acceptable battery life. 1 hour drive time * 50A = 50Ah supplied by vehicle, 70Ah required by charger over night @ home. Assuming minimum charge time of 7 hours, you would need a 10A battery charger to ensure your batteries were fully re-charged over night. A 10A battery charger ranges from $50 to $400.
If you drive more and work less you might save on batteries and the charger.
Finally, the $100 for the "design". The national average for EE's is slightly over $100k/year. Assuming 50 weeks/year @ 40hrs/week this implies $50/hr, generally with benefits. An "off the cuff design" to replace you having to switch the heater on and off might take a couple of hours, a formal design could easily take 20 hours, a full-blown, safety approved, production design could take well over 100 hours. Having a single unit built from any of the above designs could easily run $1000. My point is, keep it simple. Just because 10,000 "boxes" could be designed and built to retail for $50 each, does NOT imply that a single unit could could be designed built for $500. That is the nature of mass production. $10,000 in engineering is only $1/10,000 units or $0.10/100,000 units, but if you only need 1 unit, it is $10,000/unit.
Anyway, it looks to me like you can "save" on extension chords by purchasing $100-$300 worth of batteries, $70 on an inverter and $50-$400 on a charger. With a 25ft extension chord running ~$10, what you have to ask yourself is: "Am I losing 22 to 77 extension chords a year?"
Fish