True, chemical energy is concentrated, more so than most mechanical energy (except for meteoroids and similar), but less so than nuclear energy.
In fusion reactions, tunnelling is equally important as thermal energy. Very few D and T nucleus have enough time kT to get close enough: this is improbable. But they're helped a lot by tunnelling, which is improbable as well but reduces even more the unlikeliness of fusion by the sole thermal energy. In fact, fusion uses both with about equal unlikeliness.
Bringing D and T to 5fm (one nucleus diameter) distance would demand 300keV (3e9 K) while tunneling reduces it to 20keV (2e8 K).