Overheated is the third mission of the first episode in Prismata. Complete all the missions of the episode to unlock the expert mission challenges. This mission consists of three basic defensive survival puzzles, where you have to defend only until the Overheat Ray takes out your opponent's units, after which a new challenge starts. Below are hints and the solution for each.
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The best immediate absorb is not always the best (see Defensive strategies) when a few turns are considered. Generally, it is important to figure out which optimal outcome you will have in the next turn too: In the shoes of your opponent, what is the defence that would be terrible to go against? In this mission you can sacrifice drones to that end.
Defending with a wall is more cost-efficient than using engineers (5 gold for 3 +absorb instead of 6 gold for 3 health). Every now and again engineers might be a better buy to keep absorbing damage in upcoming turns and spend all the money available: Set yourself up with an odd numbered gold income for alternating amounts of buyable engineers for turns with an even numbered gold bank.
The puzzles are set up in ways that often make the unintuitive play the correct one.
Victory window message
Phase 3 of this challenge has two different solutions (spoiler removed, see starting turn for challenge 3)
Challenge 1[]
Info: To assign attack/defence automatically press the Q key. Marked here with (q)
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Turn 1: defend without losing an engineer
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Turn 1: Click all drones (q) Build W, defend without losing the engineer (keeping two energy matrices alive).
Turn 2: Click all drones (q) WW
Turn 3: W and sacrifice most drones
Turn 4: win
Challenge 2[]
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You cannot build engineers to optimally absorb in this puzzle. Use drones for that purpose.
On the last turns you have to sacrifice a lot to keep the Overheat Ray alive.
Not having Blastforges available and not having to live/fight after the Ray shoots simplifies how to assess efficiency and calculate income and costs. Here you can build both Drones and Engineers. They are equally efficient as defenders as soon as the Drone gets clicked once before blocking (net cost of 2; note the difference between start of turn and click). So you need a drone alive for more than 1 turn (that's more than 2 from the point you paid for it) to more than break-even.
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As walls are the most efficient blocker you have (same Health in Engineers costs you 6gold plus build time), you will want to use the most of your Behemium.
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Towards the end you will deal with 13 and 14 damage. If you are set up to optimally absorb these waves you will succeed.
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Don't drone up more than to 14. (for the solution described here)
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Turn 11: Build DD (another solution, as per victory screen message, starts with DDE)