Is it better to run a 24V tec on 12V supply if no controller is available?
The voltage rating of a TEC is that which gives you the highest temperature difference. However, the highest COP (coefficient of performance, aka efficiency) generally comes in at somewhat less than 50% of that rating). Therefore it's likely that a 24v TEC run at 12v will give much higher efficiency than one run at its nominal rating.

Efficiency in a TEC system is critically dependent on reducing the temperature difference, so a good cold side is worth improving. Water cooling is often useful. Consider an evaporative (swamp, bong) cooler for reducing the cold side to below ambient efficiently.

There is a TEC manufacturer's site somewhere on the web that has a tool that allows you to optimise the choice of TEC and drive voltage for 'smallest TEC', or 'lowest power consumption', I don't recall whether there are other optimasation criteria. I'll try to find it and update this answer, though happy to receive comments pointing to it.