Before we begin, allow me to shell out five dollars for that word. I have to do that every time I use it (which isn't often), but it's worth it.
From a Greek root meaning "to find or seek out", the heuristic way of life is indeed a rewarding one. Think of it as a trial-and-error process of making your way through the world--with the information God has revealed--and an open mind and heart for more.
As Christians, having taken in the information of God's existence and Jesus' atonement and love for us, where do we go from there? Do we, as Jiminy Cricket exhorts, "always let our conscience be our guide"? Sure. But that's not quite enough. Conscience is subjective, each individual's being more-or-less sensitive than the another's. As Jesus said, the Holy Ghost "shall teach you all things..." (John 14:26). He "searches all things, yea, the deep things of God" (1 Corinthians 2:10). This thrills me to no end. To know that there are vast vistas and depths to God's love and character and creation that He will reveal to anyone who will humble themselves and be "led by the Spirit of God." (Romans 8:14). And don't think me New Agey (we'll get into that in a moment) or weird. It's going to take us all of eternity to know God the Father. And as we are living for eternity right now, why not get to know Him as well as we can--right now?
The subtitle of Carl Sagan's book "The Demon-Haunted World" reads: "Science as a Candle in the Dark". This is a heuristic process. Taking what we know of the natural world and using that knowledge to illumine the inherent mysteries of life. Just the physical, mind you. He, in his video series entitled "Cosmos", proclaims with robust confidence that "the universe is all that is, and was and ever will be." I see what he's saying yet through his unbelief and unwillingness to consider more information, he missed God completely. Scientific Materialism is not all there is. Take in more information.
Yet the spiritual divorced from fellowship with Jesus is just as dangerous, if not more so. Case in point: Rudolf Steiner, founder of the Waldorf School and also the discipline of Anthroposophy purports that through it, we can (heuristically) seek out and understand the divine mysteries--on our own. Wait a minute. Paul says that things are "revealed unto His holy apostles and prophets by the Spirit (Ephesians 3:5, emphasis mine). Without the Holy Spirit as our guide, we most definitely be led astray and deceived. Again, the information of Jesus and what He did for us on the cross is ignored and passed over. When we don't (heuristically) take everything to God by "acknowledging Him in all our ways", (Proverbs 3:5-6) then we shut out the illumination of the Holy Spirit in our lives.
Don't ever stop being curious. Curiosity is a gift from God. If you need answers, however, then invite God with you on your quest, taking each piece of revealed information and letting God build you up. But before you go, come to Jesus and, as He says in Matthew (11:28), take my yoke upon you, and learn of me. " Be willing to sit and listen first. And He will either fulfill your curiosity as He did for Daniel (10:12) and Jeremiah (33:3) or lay it to rest for another time with His peace "which passeth all understanding." (Philippians 4:7)
"The secret of the Lord is with them that fear Him; and He will shew them his covenant." (Psalm 25:14)
And here's twenty bucks.