That is a reply to General James H Van Alen, source linked below (the letter that Lincoln is replying to has never been found.) https://quod.lib.umich.edu/l/lincoln/lincoln8/1:872?rgn=div1;view=fulltext

Lincoln was moderate in his politics, radical republicans constantly bemoaned his lack of more extreme measures and plans for reconstruction.

Radical republicans were already angry at his use of a pocket veto to shoot down the Wade-Davis Bill and its “Ironclad Oath” requirement and further more by his own Reconstruction Proclamation.

Lincoln’s stance on reconstruction is best summed up in his last public address (3 days before the letter you’re asking about). The context for the below quote is the demand for harsher measures of re-admittance and the legitimacy of Louisiana’s new state government.

“…we shall sooner have the fowl by hatching the egg than by smashing it?” https://quod.lib.umich.edu/l/lincoln/lincoln8/1:850.1?rgn=div2;singlegenre=All;sort=occur;subview=detail;type=simple;view=fulltext;q1=Sooner+have+the+fowl

I can’t find anywhere else that Lincoln has used the phrase “hearts and hands”, but his letter does say that he’s borrowing the recipients own words. Without Van Alen’s letter and the context it would bring, it’s not prudent for me to say exactly what Lincoln meant in his use of that phrase.

Without offering personal speculation or interpretation, I think it’s important to look at Lincoln’s vision for reconstruction and reconciliation.

• The letter he is (supposedly) replying to is asking him to avoid exposing himself to danger.
• Lincoln was trying to bring rebel states and peoples back into the folds of the union, while battling extreme proposals of radical republicans.
• Lincoln’s stance on reconstruction was about ceasing hostilities and speedily readmitting the southern states.

Hope this offers the context you’re looking for!