Ok, Thermopylae, here goes…
Gaming system – reasonably irrelevant. You could shoehorn it into pretty much any game system you wanted but Lion Rampant or something similarly streamlined might be an easy enough starting point.
Set the game up with a limited frontage where the opposing forces can fight (obviously…) with the choke points and Greek forces deployed closer to one edge so that the Persian forces have control of most of the board, maybe about a 1/3 vs 2/3 split.
For the Greeks, as @avernos suggested fatigue will be key, so Greek forces will need to track fatigue and damage. Fatigue would increase when a unit is engaged in combat (maybe 1 point a round on the fatigue tracker) and extra fatigue is gained when a Greek commander pushes a unit to engage in heroic feats of arms (i.e. using a command to permit a reroll or something similar). Fatigue could be reduced by rotating troops out of the front lines and allowing them time to recover at the back of the Greek lines (Maybe recovering a point of fatigue each round on a 4+ or a 5+ depending on what modifiers you wish to use). Troops could only rotate out of combat and retire to the back ranks when not engaged. Cumulative fatigue will impose combat penalties at various tiers (these will vary depending on your games system of choice).
For the Persians, track both wounds and morale for each unit (The Greeks don’t need to track morale as we can assume that the Spartans are resigned to their fate and the remainder will withdraw once the Spartans are defeated. Similarly, the Persian troops have sufficient numbers that fatigue is not an issue – fresh forces can cycle in as required). Additionally, track cumulative morale points overall on a separate army tracker. This is effectively the Greek ‘win’ condition. If the Persians Accumulate enough morale points and can be so psychologically scarred at being stopped by a few hundred Greeks then they will be less motivated to try and engage all the city-states of Greece in open war later on.
Persian forces will recycle. Objective of the Persian player is to manoeuvre reinforcing units in such a way that they can move in to plug gaps as their attack becomes dulled and prevent Greek units form retiring and resting, with the obvious intent being to keep them in place and grind them down or even break through the lines. Persian units we can assume will be likely to break when they accumulate enough morale points, with fleeing units potentially disrupting the advance of fresh troops. Overall win condition will be based on the destruction of the Greek forces before the army morale tracker gets too high.
Greek forces will need to manage fatigue, placement of reserve units and have strategic use of fatigue causing rerolls or special unit activations. For added fun, have a few healers or similar characters about who can remove a fatigue point from a nearby unit each round.
To spice things up, you could have Persian archers trading fire with Greek slingers or javelin throwers over the front lines. Alternatively, if you want to go full movie 300 (blood splatter and slow motion camera effects optional..) you could introduce some of the more exotic Persian units who could have in-game effects like adding fatigue to a unit instead of, or in addition to, standard damage. Or perhaps imposing combat penalties on a unit for a number of rounds.
If a timer is deemed necessary you could have a day last a set number of turns. Once darkness falls the Persians fall back and regroup and the Greek force recovers a set number of fatigue points overnight (not all of them – we can assume they are continually harassed by Persian scouts). The game could end perhaps partway through day 3 when the Greeks become surrounded if they have not been defeated earlier? (I’d count this result as a Greek victory).
I’m sure there are much more elaborate card based mechanics that could be employed to represent the intervention of force commanders or access to elite status units for the Persians, but the above is how I’d go about approaching it from a more simplistic dice and miniature background.