I was just recently looking at oscillators with low heat. Burloaferimeter with heat 10/7 ≈ 1.43 is the only known oscillator with heat below 2. However, oscillators with heat greater than but arbitrarily close to 4/3 ≈ 1.33 almost certainly exist. This is because the 2c/3 half-signal has heat 4/3.
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x = 38, y = 40, rule = B3/S23
6b2o2b2o2b2o$6b2o2b2o2b2o2$4b12o$3bo12bo$3bob12o$2obo15bo$2obo2b14o$3b
obo$3bobo2b14o$2obobobo14bo$2obobobo2b13o$3bobobobo15bo$3bobobobo2b14o
$2obobobobobo$2obobobobobo2b14o$3bobobobobobo14bo$3bobobobobobo2b13o$
2b2obobobobobobo15bo$5bobobobobobo2b14o$5bobobobobobobo$4b2obobobobobo
bo2b14o$7bobobobobobobo14bo$7bobobobobobobo2b13o$8b2obobobobobobo15bo$
11bobobobobobo2b14o$11bobobobobobobo$10b2obobobobobobo2b2o2b2o2b2o$13b
obobobobobobobo2b2o2b2o$13bobobobobobob2o$14b2obobobobo$17bobobobo$17b
obobobob2o$16b2obobobob2o$19bobobo$19bobobo$20b2obob2o$23bob2o$23bo$
22b2o!
A low-heat oscillator would work by reflecting a single half-signal to form a "loop". The difficulty is that the orientation of the half signal must be flipped on the second pass through the loop. This might require the injector and receiver ends of the wire to be completely reconstructed after each pass of the signal to work with the opposite orientation on the next pass. However many cell changes this reconstruction requires can be made up for by extending the length of the 2c/3 wire to get the overall heat arbitrarily close to the half-signal heat of 4/3.
Of course, this all assumes that half-signal injectors and receivers exist, along with a way to reconstruct the ends of the wire so that they can inject/accept an oppositely oriented signal on the second pass. It seems almost certain that these things exist, although I'm not sure how likely it is that we can find them.
So there are almost certainly oscillators with lower heat than burloaferimeter, but it's not clear if there are any oscillators with heat 4/3 or lower.
Edit: since this is the unproven conjectures thread, I'll make my conjecture explicit:
Conjecture: there are no oscillators with heat less than or equal to 4/3.
