Your question is quite "interesting", but OK, here is your answer: You need to check bytecode.
Here is bytecode of method 1:
public method1()V
   L0
    LINENUMBER 10 L0
    ALOAD 0
    GETFIELD package/SomeClass.myList : Ljava/util/List;
    INVOKEINTERFACE java/util/List.iterator ()Ljava/util/Iterator; (itf)
    ASTORE 1
   L1
   FRAME APPEND [java/util/Iterator]
    ALOAD 1
    INVOKEINTERFACE java/util/Iterator.hasNext ()Z (itf)
    IFEQ L2
    ALOAD 1
    INVOKEINTERFACE java/util/Iterator.next ()Ljava/lang/Object; (itf)
    CHECKCAST java/lang/String
    ASTORE 2
   L3
    LINENUMBER 11 L3
    ALOAD 0
    GETFIELD package/SomeClass.myList : Ljava/util/List;
    ALOAD 2
    INVOKEINTERFACE java/util/List.indexOf (Ljava/lang/Object;)I (itf)
    ISTORE 3
   L4
    LINENUMBER 12 L4
    GETSTATIC java/lang/System.out : Ljava/io/PrintStream;
    ILOAD 3
    INVOKEVIRTUAL java/io/PrintStream.println (I)V
   L5
    LINENUMBER 13 L5
    GOTO L1
   L2
    LINENUMBER 14 L2
   FRAME CHOP 1
    RETURN
   L6
    LOCALVARIABLE index I L4 L5 3
    LOCALVARIABLE key Ljava/lang/String; L3 L5 2
    LOCALVARIABLE this Lpackage/SomeClass; L0 L6 0
    MAXSTACK = 2
    MAXLOCALS = 4
Here is bytecode of method 2:
public method2()V
   L0
    LINENUMBER 12 L0
    ALOAD 0
    GETFIELD package/SomeClass2.myList : Ljava/util/List;
    INVOKEINTERFACE java/util/List.iterator ()Ljava/util/Iterator; (itf)
    ASTORE 2
   L1
   FRAME APPEND [T java/util/Iterator]
    ALOAD 2
    INVOKEINTERFACE java/util/Iterator.hasNext ()Z (itf)
    IFEQ L2
    ALOAD 2
    INVOKEINTERFACE java/util/Iterator.next ()Ljava/lang/Object; (itf)
    CHECKCAST java/lang/String
    ASTORE 3
   L3
    LINENUMBER 13 L3
    ALOAD 0
    GETFIELD package/SomeClass2.myList : Ljava/util/List;
    ALOAD 3
    INVOKEINTERFACE java/util/List.indexOf (Ljava/lang/Object;)I (itf)
    ISTORE 1
   L4
    LINENUMBER 14 L4
    GETSTATIC java/lang/System.out : Ljava/io/PrintStream;
    ILOAD 1
    INVOKEVIRTUAL java/io/PrintStream.println (I)V
   L5
    LINENUMBER 15 L5
    GOTO L1
   L2
    LINENUMBER 16 L2
   FRAME CHOP 2
    RETURN
   L6
    LOCALVARIABLE key Ljava/lang/String; L3 L5 3
    LOCALVARIABLE index I L4 L2 1
    LOCALVARIABLE this Lpackage/SomeClass2; L0 L6 0
    MAXSTACK = 2
    MAXLOCALS = 4
If you do the diff (diffchecker for example), you will see that BYTECODE IS THE SAME (optimized by compiler)- so is the performance.
Anyway, as @erwin-bolwidt correctly noted, performance problem is using indexOf method in for loop, not place of declaring local variable.