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",
        "canSpeedyJump"
      ]
    },
    "canIBJ",
    "canTrickyDashJump",
    {
      "and": [
        {
          "canShineCharge": {
            "usedTiles": 28,
            "gentleUpTiles": 3,
            "gentleDownTiles": 3,
            "openEnd": 0
          }
        },
        {
          "or": [
            {
              "shinespark": {
                "frames": 18,
                "excessFrames": 8
              }
            },
            {
              "and": [
                "canSpeedyJump",
                {
                  "shinespark": {
                    "frames": 16,
                    "excessFrames": 10
                  }
                }
              ]
            }
          ]
        }
      ]
    }
  ]
}
"h_heatedGModeOpenDifferentDoor"