In this way, should washing machine door feel warm?
No Heat In The Door Or Laundry With modern machines and low temperature washes, which is what most people do, you will generally speaking not feel much if any heat through the door glass. And, when you do it's only on the wash part of the cycle.
In this way, do washing machines get hot?
For cycles with high temperatures (usually above 60 degrees), front-loading washing machines use a washing heater. Therefore, the exterior gets hot as internal temperature rises. Washing machine can get hot during operation, this is completely normal.
In general, assume no. If you want a warm-water wash with a broken hot water heater, heat up some water on the stove and pour it in as the machine is filling. On the other hand, you might find that you can get perfectly decent results with cold water.