Burning away dross reveals inner holiness

מצות הרמת הדשן כי כפי מה שנשרף הפסולת.

The mitzvah of terumas hadeshen (the removal of the ashes): for according to the measure in which the refuse is burned,

The Sefas Emes draws a lesson from the mitzvah of removing the ashes of the altar: the burning away of the "refuse" is itself meaningful avodah.

כמו כן מתגלה הקדושה באדם.

so too does the kedushah become revealed within man.

The more a person burns away the dross within himself, the more his inner holiness is uncovered and revealed.

כי יש מ"ט פנים טהור וטמא.

For there are forty-nine "faces" (aspects) of pure and of impure.

There are forty-nine facets of purity and, paralleling them, forty-nine facets of impurity — two opposing arrays within reality.

ויש בלב איש ישראל ג"כ מ"ט שערים.

And in the heart of a Yisrael there are likewise forty-nine gates.

Corresponding to those facets, the heart of a Jew contains forty-nine gates of its own, each a portal of inner avodah.

וכמ"ש הלב מבין.

As it is said, "the heart understands."

The heart is the seat of understanding, the place where these inner gates of binah are opened.

ויש עלי' גם למחשבות זרות באם נשרפין בעת עלותם על רוח האדם.

And there is an ascent even for foreign thoughts, if they are burned at the moment they arise upon a person's spirit.

Even machshavos zaros (alien, distracting thoughts) can be elevated — provided that when they surface, a person immediately "burns" them in the fire of his longing for Hashem rather than entertaining them.

כמ"ש היא העולה מחשבה רעה דאתוקדא ע"י שעולה בלהב המזבח שהוא הבל הלב שצריך להיות מתוקד בו תמיד אש התשוקה לה'.

As it is said, "it is the olah (the elevation-offering)" — an evil thought that is consumed by rising in the flame of the altar, which is the breath of the heart, in which the fire of yearning for Hashem must always be kept burning.

The "olah," the offering that goes up entirely, alludes to an evil thought consumed and lifted up by the flame of the inner altar — the "breath of the heart" — where the fire of constant yearning for Hashem must perpetually burn.

ואז מתרומם זה הדשן כנ"ל כמובן:

And then this "ash" is lifted up, as above, as is understood.

When the alien thought is burned in that inner fire, even its residual "ash" is elevated — just as the terumas hadeshen lifts up the ashes of the altar.

Summary: The mitzvah of terumas hadeshen teaches that as the refuse is burned, holiness is revealed within man. Corresponding to the forty-nine facets of pure and impure, the heart of a Jew holds forty-nine gates, for "the heart understands." Even foreign, evil thoughts can be elevated if, the moment they arise, they are consumed in the flame of the inner altar — the breath of the heart, where the fire of constant yearning for Hashem must always burn — so that even the resulting "ash" is lifted up.