Japanese bento boxes are traditionally eaten at room temperature.  
However, we’ve found the following heating instructions helpful especially in winter time.

Microwave:

  1. Remove the lid (not microwaveable).
  2. Remove big paper cup (salad) and small paper cup (pickles) from the bento box prior to microwaving the entrée. Remove small paper cup (pickles) from the bowl.
  3. Cover with a paper napkin or towel.
  4. Microwave for about 1 minute and 10 seconds.

Conventional Oven:

  1. Remove the lid.
  2. Remove big paper cup (salad) and small paper cup (pickles) from the bento box prior to microwaving the entrée. Remove small paper cup (pickles) from the bowl.
  3. Transfer items to be heated to an oven-safe container.
  4. Cover with parchment paper or aluminum foil.
  5. Preheat oven to 300 °F and heat for about 3 minutes.

About compostable containers:

Fiber container:

Made from bamboo and unbleached plant fiber. These disposable food containers are certified compostable, eco-friendly, soak proof, freezer safe, and contain no wax or plastic lining. Composts in 2 to 4 months in a commercial composting facility.

https://store.worldcentric.com/10x7x5x1x5-29-oz-fiber-container-3-compt

Compostable clear lid:

Made from plants grown in the USA. They are suitable for liquids up to 120°F, freezer safe and compost in 2 to 4 months in a commercial composting facility. Even though they are as light and strong as plastic, these disposable lids fully break down when commercially composted. Not microwavable.

https://store.worldcentric.com/lid-pla-10x7x5-fiber-container-clear-3-compt