In short, scripture speaks against this idea of requiring a heart for the work. Notably, Jesus did not caveat the great commission so it reads "go and make disciples of all those for whom you have a heart... those you particularly like". Rather, it reads "Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit (Mt 28:19, ESV)". Significantly, Jesus continues and says "teaching them [those of whom you make disciples] to observe all that I have commanded you (Mt 28:20a, ESV)", which presumably includes this bit about going into all the world and making disciples. There was certainly no sense from Jesus that the apostles had to figure out for whom they had a real heart and to focus their attentions solely on them - they were told quite directly to reach all nations.
The book of Jonah frames this issue in an alternative way. The Lord commanded this prophet to go to Nineveh and, we can safely conclude from his response, Jonah did not have a heart for these people (Jon 1:3-16). In fact, Jonah so despised the people of Nineveh that he was prepared to die rather than reach them with God's message (Jon 1:12). Having been humbled by God and eventually taken the Lord's message of judgement to this city, Jonah is apoplectic when God relents at seeing Nineveh turn from its sin (Jon 4:1-3). Far worse than not "having a heart" for these people, Jonah wanted the city of Nineveh to be destroyed. He specifically did not want to take the Lord's message to them because he knew God was gracious and would relent from disaster were the people to repent. It is interesting that God saved a whole city despite the messenger holding the people in contempt and actively hoping for their destruction. It appears God can, and will, work even when our hearts are not really in it.
So, do we need a specific "heart" for peoples and areas before we can engage in reaching them? Scripture doesn't make this a caveat for evangelism. In fact, the Bible suggests we should reach whomever we have the ability to reach. Paul was clear about where his focus lay. He says:
For though I am free from all, I have made myself a servant to all, that I might win more of them. To the Jews I became as a Jew, in order to win Jews. To those under the law I became as one under the law (though not being myself under the law) that I might win those under the law. To those outside the law I became as one outside the law (not being outside the law of God but under the law of Christ) that I might win those outside the law. To the weak I became weak, that I might win the weak. I have become all things to all people, that by all means I might save some. I do it all for the sake of the gospel, that I may share with them in its blessings (1 Cor 9:19-23).Therefore, where opportunities are granted to us to share the gospel the question of whether we have "a heart" for the area or people should be moot. We should all have a heart for the lost, whomever they may be, because the Lord has a heart for them (2 Pet 3:9), just as he had a heart for us when he died to save us (Rom 5:8).