In this kind of situation cold flows from cold to hot, from cold outside to hot inside the shoe. The clip fitting is an ideal channel. So, insulation in that area will help.

You say only the soles of your feet were cold? Common problem for everyone is cold climates. That is why cold weather boots have thick soles; not those pseudo cold weather boots sold in many stores. So, take a lesson from them. Thicken up your soles by inserts. Additional heaters, etc. won't solve that particular problem.

You may have to buy larger shoes/boots to accommodate the extra insulation and still allow adequate blood/lymph circulation. At that point you may well want to consider going to a bear claw style pedal and just using a standard winter boot. That is what most people I know have done.

Heaters sound good. But, they are a hazard in themselves. Accidentally touching the skin with them can cause burns. Relying on them and having a delay getting to warm when they run out can cause cold injury. I use them; but with a great deal of caution.

Whatever you do you MUST keep your feet dry. If you sweat a lot, like many people, stopping to change your socks every hour or so is a great idea. Even a planned short ride mandates carrying extra socks just in case.

Of course I'm coming at this from the perspective of someone who has spent days outside in below freezing temperatures and who has had to handle cold injuries from people who didn't know enough to make proper provision. If you are in a warm climate and only riding around the block just gutsing it out may work.