Yes.
The glass and plastic cups can be heated to 120 degrees. Be sure to remove the lid, it will melt if heated in the microwave.
A note of caution with glass tumblers. You cannot heat liquids in the microwave above boiling point, it will cause them to shatter with temperature changes.
Do not microwave KeepCup Brew Cork Edition, it will accelerate the deterioration of the cork band by drying it out.
The tritan booster on LongPlay will warp and crack if heating above 110 degrees.