In addition to the other really good advices you can find here:

My opinion is that your player does not perceive the dungeon as a dangerous place to be. If you can make this change, all your players will react accordingly.

Examples:

• let them meet an "adventurer hero superstar" outside the dungeon, which is much more powerful and well known than the characters, just to found his corpse later inside the dungeon with a tiny hole on the neck, inside an empty room.

• prepare an apparently empty dungeon. For the first part describe accurately the environment, give sinister detail of the rooms, strange sounds, false alarms, horrid books... but no monster at all (for the first part).

• place the signs of recent passage of a monster notoriously too strong for them (only clues and tracks, they will meet him only if they act really stupid).

• make a different section of the dungeon look more menacing (darker, unholy runes on a door, spider's silk/blood everywhere, warped walls) if possible with a dark story, just to send a clear message: from now on shit got serious.

• make a trap spottable without a check at the start of the dungeon (because of a damaged door or something like that) and then put a really nasty effect on it. Only stupid characters will activate it, and your duty as a DM is to make him regret that.

• make a section of the dungeon where you can enter and cannot escape easily where ALL kind of healing does not work.

These and some more evil DM techniques should make the characters worry and think about their HP as a limited precious resource rather than a big safe number.

Extra:

• if you fear to hit "good players" place a low DC to spot/disarm the traps
• explain how the discovered trap works, so the players can pass through without activating it and use it to their advantage luring stupid monsters inside.
• make some of the traps of the dungeon that deal permanent damage (a damage type you can heal only with some really expensive spells)
• make a trap that makes a cage fall off the ceiling/make appear a pit, followed by monsters, armed with ranged weapons, giving them a large edge in the fight.
• talking about pits... why not acid/lava pool traps? you have an armor huh? what about a swim check to avoid drowning, too?

I hope this helps :)

In addition to the other really good advices you can find here:

My opinion is that your player does not perceive the dungeon as a dangerous place to be. If you can make this change, all your players will react accordingly.

Examples:

• let them meet an "adventurer hero superstar" outside the dungeon, which is much more powerful and well known than the characters, just to found his corpse later inside the dungeon with a tiny hole on the neck, inside an empty room.

• prepare an apparently empty dungeon. For the first part describe accurately the environment, give sinister detail of the rooms, strange sounds, false alarms, horrid books... but no monster at all (for the first part).

• place the signs of recent passage of a monster notoriously too strong for them (only clues and tracks, they will meet him only if they act really stupid).

• make a different section of the dungeon look more menacing (darker, unholy runes on a door, spider's silk/blood everywhere, warped walls) if possible with a dark story, just to send a clear message: from now on shit got serious.

• make a trap spottable without a check at the start of the dungeon (because of a damaged door or something like that) and then put a really nasty effect on it. Only stupid characters will activate it, and your duty as a DM is to make him regret that.

• make a section of the dungeon where you can enter and cannot escape easily where ALL kind of healing does not work.

These and some more evil DM techniques should make the characters worry and think about their HP as a limited precious resource rather than a big safe number.

Extra:

• if you fear to hit "good players" place a low DC to spot/disarm the traps
• explain how the discovered trap works, so the players can pass through without activating it and use it to their advantage luring stupid monsters inside.
• make some of the traps of the dungeon that deal permanent damage (a damage type you can heal only with some really expensive spells)
• make a trap that makes a cage fall off the ceiling/make appear a pit, followed by monsters, armed with ranged weapons, giving them a large edge in the fight.
• talking about pits... why not acid/lava pool traps? you have an armor huh? what about a swim check to avoid drowning, too?
• many many Health points? hit an ability score that is precious to that particular character, or even all...

I hope this helps :)