{TMainForm}
 
  type
    TMyThread = class(TThread)
      type TThreadMethod = (tmExample, tmRead, tmCreate);
      var tm: TThreadMethod;
      var w: OLEVariant;
    private
      function CreateExample(): boolean;
    protected
      procedure Execute(); override;
      constructor Create(const tmValue: TThreadMethod);
      destructor Destroy(); override;
  end;
 
var thread: TMyThread;
 
procedure TMainForm.FormDestroy(Sender: TObject);
begin
  FreeAndNil(thread);
end;

procedure TMainForm.Button3Click(Sender: TObject);
begin
  thread := TMyThread.Create(tmExample);
end;

{ TMyThread }
 
constructor TMyThread.Create(const tmValue: TThreadMethod);
begin
  Synchronize(MainForm.Lock);
  Self.tm := tmValue;
 
  inherited Create();
end;
 
destructor TMyThread.Destroy;
begin
  Synchronize(MainForm.UnLock);
 
  inherited;
end;
 
procedure TMyThread.Execute;
begin
  inherited;
 
  try
    if CoInitialize(nil) <> S_OK then raise Exception.Create('Ошибка при инициализации COM!');
 
    try
      w := CreateOLEObject({someobject}); // Здесь поток долго думает (секунд 20), затем выдаёт ошибку EOleSysError
 
      if tm = tmExample then
        if not CreateExample() then //working with `w`
          raise Exception.Create('Ошибка при работе с OLE!');
    except
      //some error dlgmsg
    end;
  finally
    CoUninitialize();
  end;
 
  Free;
end;

begin
  t := TTask.Create(
    procedure
    var w: OleVariant;
    begin
      try
        OleCheck(OleInitialize(nil));
 
        w := CreateOLEObject({someobject}); // та же ошибка
        w.Visible := true;
 
        //some work with `w`
 
        //complete msg
      except
        //error msg
      end;
 
      OleUninitialize();
    end
  );
 
  t.Start();
end;