Step 1: Picture the baked zone.
The hot dolerite dyke bakes the schist beside it. The temperature is high right at the contact and falls as we move away, so 2 metres out the heat is only moderate.
Step 2: Use the rock chemistry.
The schist is rich in boron and carries mica and chlorite. With heat plus the water it releases, this mix favours hydrous minerals.
Step 3: Pick the right new mineral.
At a moderate distance the contact heat grows amphibole, a hydrous mineral typical of medium grade baking of schists. So amphibole develops there.
Step 4: Reject the others.
Orthopyroxene and clinopyroxene need very high, dry heat found only at the contact itself. Tourmaline is a pegmatite mineral, not a contact baking product. So those do not fit 2 metres out.
Step 5: Final choice.
So the mineral that forms is amphibole.
\[ \boxed{\text{Amphibole}} \]