We cannot truly love people and not give them Jesus.Our actions matter too, don't get me wrong. Saying "don't be hungry" but doing nothing is lame. Faith is evidenced by works. See James 2 Let me say it again, Faith is evidenced by works. Actions are an overflow of faith. Faith would not be faith if it wasn't voiced at some point in the context of the action.
It is the cup of cold water given in Jesus' Name that we will be rewarded for.Give God credit for the hope that you have. Don't copy and paste His words carelessly. Legally that's copyright infringement. If we leave Jesus off then we are loving in our own strength and sooner or later that "love" will run dry.
It isn't possible to love people conveniently.Love is always a choice. The truest love always a sacrifice. "Sacrifice" and "Convenience" don't belong in the same sentence. (Unless of course you're observing how they don't belong in the same sentence ... )
What motivates sacrificial love?For me it's knowing Christ wants to love someone through me. It's appreciating the chance to show them His love. Only it never comes naturally. Like a fine gourmet meal, the best love takes preparation and skill. Because of those two it seems natural. If you're challenged receiving, knowing, or giving love remember ... God is Love. Don't separate the "Love of God" from God. So if you're struggling ask for help. Jesus Himself will flow into you with better love and better words than you yourself could think, hope or wish for.