This is how I would fully engineer the Asp for exploration. Some notes about this:
(a) The FSD has optimal mass 1856.40 T. This is higher than the class 5 long range / mass manager FSD -- I am using the CG double engineered FSD. You can get them from any human technology broker. Make sure to put mass manager on them.
(b) Supercruise assist. I think this is an important module for the type of exploration I do, where I map all terraformables, earth-likes, ammonia planets, and water worlds, even if they are far from the main star in a system. Supercruise assist makes it less tedious to get to those bodies in a system.
(c) No shield. I think explorers don't need shields. The usual reasons people cite for needing them is: (i) player interdictions, (ii) NPC interdictions and (iii) avoiding bumps when doing planetary landings.
I explore in Solo, especially when returning from a trip. Some play in Open, in which case I suggest contacting player groups that provide escorts to returning explorers, and/or add a strong shield+boosters and good thrusters to your build -- to give yourself time to escape an interdiction (although the Asp is not a very fast ship compared to the Dolphin, the Phantom, or the Orca, which are other popular exploration choices). So for me (i) is irrelevant. I have never lost to an NPC interdicting in an Asp, Krait or other medium ship -- it's always possible to evade. So (ii) is irrelevant. If you are rusty on avoiding interdictions do some missions when they send ships after you, and practice. It's quite easy. As far landings, it's quite simple to land without doing any hull damage carefully toggling FA OFF while keeping the ship horizontal. It's quite easy to do even on high G planets like Achenar 3 (I did it a few days ago as a test). Try it!
(d) Heat sink. Some people don't use them. In my experience it is definitely the case that some rare double and triple star systems, if jumped into from certain angles, would require a heat sink to avoid damage.
(e) Class A life support. Some explorers recommend class D because it is lighter. I think a nominal loss of jump range is worth it for having 25 minutes of oxygen if the canopy breaks. That and synthesis for more life support, combined with the DSSA carriers basically guarantees survival even if your canopy breaks in deep space.
(f) Clean thrusters with stripped down. Some people advocate dirty drives and drag drives. I think clean drives are better for being naturally stealthy out of supercruise (which comes in handy if you mess around with lifeforms or thargoids in space). I think this would probably run 10 or 11% heat with thrusters at full power. I don't think you ever need to outrun anything out of supercruise when exploring, if you avoid NPC interdictions, and play in Solo. Some people run dirty drives/drag drives because they want to zoom around on a planet or something -- that's fine if you like that, but it's more weight and less jump range.
(g) Repair limpet controller 1D + cargo rack. If you are doing a long term exploration mission, you probably want these as insurance for hull damage. If you want to mess around with lifeforms consider decontamination limpet controller 3D -- repairs about as much as repair limpet controller 1D and also handles caustic damage some lifeforms can do. Don't bring limpets with you -- it's extra weight you don't need. Instead, synthesize them if needed.
(h) 1D power distributor. Explorers don't need to boost over and over again (although this one will let the Asp boost if engine focused). To save energy and run a bit cooler, you can always turn off the power distributor after putting 4 pips into engines -- you never need another pip configuration as an explorer without shields and weapons, and the distributor "freezes" the last configuration you used even if it is turned off.
(i) 3A low emissions / stripped down power plant. Once you add the Guardian FSD booster, there is no practical way to get away with a 2A power plant on the Asp without running armored. But Asp is a fairly hot-running ship, so the low emissions power plant really helps with that. I think it's worth the small loss of jump range. D power plants are out of the question for explorers, because they run very hot. 3A gives you a bit of a cushion in terms of available power, in case you take some power plant damage.
(j) Heavy duty and deep plating on the lightweight armor is free hull hit points (since lightweight armor is weightless). When it comes to collisions and caustic damage (the only plausible sources of damage an explorer would face), only absolute hull hit points matter, resistances do not.
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I think the Phantom is a better exploration ship overall than the Asp, these days. But the Asp has better canopy visibility, and better pitch in supercruise. And some like the way it looks better. And it's far cheaper than the Phantom, as well.