Here are your parts includes a wiring diagram.
Parts for Maytag MDE5500AYW Dryer - AppliancePartsPros.com If you click on a part's description or picture a new page will open with more info about that part.
Here is a manual. You will have to join the site and be logged in to be able to download the manual.
http://appliancejunk.com...e&id=67;t=1409823091You have to be careful that you rare looking at the correct info for your unit as the manual covers many different units.
[COLOR="Blue"]1. Does that mean the first one will reset itself after an overload?[/COLOR]
No, they are the same type of device. Once blown they stay blown.
The 3300172 is the one listed for your unit.
[COLOR="Blue"]2. I've noticed that on virtually any cycle, even air fluff, the dryer still heats up. Perhaps this indicates a failure in the thermistor/thermostat on either the blower housing or the heater element itself?
* How would I check?[/COLOR]
The thermostat is probably OK as you do get heat.
The thermistor should be about 10,000 ohms at room temperature (~70 degrees F)
I do not think either of the above is your problem.
I would start by checking the heater.
Unplug the unit and both wires at the heater.
Measure across the heater should be in the 8 to 12 ohm range.
Now measure from each side of the heater to it's case, both should be infinite ohms.
If not the heater is grounded and should be replaced.
This can cause it to run unregulated.
[COLOR="Blue"]* Say the parts on the blower side indicated a failure; would I need both #307208 and #33002567, or does the thermostat assembly contain the thermistor?[/COLOR]
No
A thermostat and a thermistor are different types of devices.
A thermostat is a set of contacts that open at a certain temperature. They then close again when the temperature drops about 20 degrees F.
A thermistor is a resistor that changes resistance as the temperature changes. This resistance is fed to an electronic board and is used by the board to regulate the temperature (basically the same as an oven probe)
3. Is there anything else I should look out for as far as things I may have done incorrectly that could cause a trip?
Start with the heater.
I cannot comment about the vent. I would suggest you check the air flow at the back of the unit with the vent off and then at the outside louver to see how much air flow you are loosing.
Also be sure to clean/check the vent system every year or so. The S will have a tendency to collect lint.
UPDATE:
Upon getting home, I tried starting it, and the drum didn't turn, but the heater did start warming up as evidenced by the smell of singed lint. So, probably not the thermal fuse. The motor and drum spin freely, so I don't think it would be the motor, but I did just have to replace the one in the washer (which had frozen completely, wouldn't turn at all).
If you do not own a meter, I would suggest you purchase a one. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.
4. When you start always short the meter leads together. This will tell you that the meter is working and if there is any 0 offset.
There is a good STICKY at the start of this forum about it's use.