There are a few options on what you can do:
1) use a larger damp towel to cover the majority of your lid.
2) use a larger water dish. Larger surface area of the water helps.
3) move your water dish to he hot side.
4) seal 80% of the lid with tin foil or something that covers most of the holes.
You can probably even cover 90-100% of the lid since the tub has a lot of air vents on the side anyway.