Yes, Captain Temporium has MFi controller support!
Captain Temporium on iOS does support controllers and is compatible with the MFI standard.
Defend yourself with the shields but always watch out that you don't run out of shield energy! Collect parachutes to get new shield energy, weapon improvements, cooling improvements, fuel for the afterburner, bonus lives or bonus score.
Don't fire at the parachutes! Watch out! The enemy could be hidden by the clouds, don't run into it! Cloud cover will increase at higher levels and overall visibility will get worse.
The boss at the end of each level can be huge, really huge! It takes many hits to kill each boss.
Try to ram the with your shields if you still have plenty of shield energy left.
Captain Temporium supports MFi controllers.