type
  TAProcedure = procedure(i: integer);

  TMyThread = class(TThread)
  private
    FAProcedure: TAProcedure;
  protected
    constructor Create(CreateSuspended: boolean; AProcedure: TAProcedure);
    procedure Execute; override;
  end;

{...}

implementation

procedure MyProcedure(i: integer); // Kopf entspricht TAProcedure
begin
  {..}
end;

{ TMyThread }

constructor TMyThread.Create(CreateSuspended: boolean;
  AProcedure: TAProcedure);
begin
  inherited Create(CreateSuspended);
  FAProcedure := AProcedure;
end;

procedure TMyThread.Execute;
begin
  if Assigned(FAProcedure) then
    FAProcedure(1);
end;

{ TfrmMain }

procedure TfrmMain.BtnClick(Sender: TObject);
begin
  TMyThread.Create(false, @MyProcedure); // passende Prozedur übergeben
end;