If I understand your post correctly, you are trying to heat a pot of soil to a temperature (75F) and then maintain it at that temperature. You want to that inside an insulated box (an old freezer) so temperature loss will be slow.
The soil will act to store heat. The water in the soil will act as a thermal conductor to distribute the heat. If you apply heat at the bottom of the via a heat pad or heat lamp the heat will naturally move up the soil. You won't need extra tubes in the soil to evenly heat it. What you want is a small heat source at the bottom that supplies enough heat to replace the heat that goes into the air at the top of the soil. This is not going to be a lot unless you turn the freezer on. Remember your soil is in a insulated box.
The washing machine drum is metal which will conduct heat all around your soil. This is a cooking pot. You put your thermostat in the soil somewhere between the heat source and the plant roots. Just remember that heat will keep moving even when you switch the heat source off.
This means that a small heat source is going to be easier to regulate than a large one. The small heat mats sold for seedlings are about 25 watts. You can leave them on a long time and they won't get very hot. The bulbs in refrigerators are about 25 watts and they are used because they won't cause the refrigerator to heat up very much while the bulb is on when the door opens. The toy ovens given to kids to play with (e.g. Barbie's oven) use a 100 watt bulb inside an insulated box and they get hot enough to bake cookies and bread. You will have to experiment with the thermostat setting and position to find where to position the temperature sensor so it maintains the desired temperature at the roots. Start with the sensor at the bottom of the pot and another thermometer at the roots. Leave the heat on so the system stabilizes (with wet soil) and notice what the difference in temperature is. It should be pretty close, maybe a few degrees difference. That will tell you the approximate temperature gradient. You should have a similar temperature difference at air temperatures within 15 or 20 degrees of what the air temp is when you measure. If the gradient is 2 degrees then you set the thermostat at 77 so the roots are 75. Now you can plant your seeds in your bespoke Dutch oven and be sure you won't be making fried tomatoes.
The other thing I see people here at Tomatoville trying to caution you about is the possibility of you killing yourself. I concur. When you wet your soil the water is going to drain out of the holes in the pot and follow gravity down, down, down, to your electrical heat source. This heat source needs to be insulated from your skin. If you have fuses or circuit breakers on your electricity source you will protect your electric wires but you can still get a nasty shock. You should always be prepared for a shock when experimenting with electricity. Wear insulated (like rubber) gloves. Use insulated tools. Always put your body in a position that will fall away from the electricity source. This is very important because you might be paralyzed from the initial shock and not be able to lift yourself off the electricity source. Any metal or wet spot of this incubator could be an electricity source. The voltage does not kill you (usually). It is the current (amperage) that literally burns you. If you have a heart condition you are in more danger. I have been shocked from poorly grounded machinery and old insulation when I was careless and ignored these rules and I consider myself lucky to survive but I don't push my luck. Neither should you.
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