It is possible to climb the left side of the room with SpeedBooster alone, with either a tricky dash jump or a vertical shinespark.

Requires:

"Morph"
{
  "or": [
    "SpaceJump",
    "canSpringBallJumpMidAir",
    "canWalljump",
    {
      "and": [
        "HiJump",
        "SpeedBooster"
      ]
    },
    "canIBJ",
    "canTrickyDashJump",
    {
      "and": [
        {
          "canShineCharge": {
            "usedTiles": 28,
            "gentleUpTiles": 3,
            "gentleDownTiles": 3,
            "openEnd": 0
          }
        },
        "canMidairShinespark",
        {
          "shinespark": {
            "frames": 17,
            "excessFrames": 4
          }
        }
      ]
    }
  ]
}
"h_heatedGModeOpenDifferentDoor"