But in order to have many atoms in the first excited level, the temperature must be high enough (around 10,000 K), but not too high. Atomic collisions cause many atoms to be in the first excited level. Then they are ready to absorb visible photons and make strong Balmer lines.
If the temperature is too low, few atoms will be in the first excited level, and there will be very weak Balmer lines. Similarly, if the temperature is too high, most atoms will be excited to levels higher than the first excited level, and again, very weak Balmer lines result.