The DAC is looking for three things: that the proposal is proportionate to the need, that it will not harm the significance of the building, and that the PCC has considered the options properly.
In practice, that means your application should show what heating you have now and why it is inadequate, what alternatives you considered and why you chose this one, how the new system will be installed (fixing points, cable routes, visual impact), and what the running costs will be. Photographs of the proposed heater locations and a simple plan drawing go a long way. If your church is listed, the DAC will pay particular attention to how visible the heaters will be and whether the installation is reversible.
The committees that cause delays are usually reacting to incomplete applications, not to the heating technology itself. A clear, well-evidenced submission that shows you have thought about heritage impact, running costs and net zero gets through far more quickly than a one-page letter asking for permission to "install some heaters". Your quinquennial inspector or architect can help you pitch the proposal at the right level.