Jukka, the only critical temperature in E-6 is that of the first developer bath. All other baths are "to completion" so if you are at 36°C instead of 38°C no problem, just prolong treatment. You basically cannot "overtreat" unless you try very hard.
That applies mainly to one-shot chemistry. If you use chemistry only once (or maybe twice at short interval) you don't worry about oxidation of chemistry and you can have it swirl a bit more in the tank. (If you reuse chemistry many times, then minimization of oxidation is a concern, and rotative processor don't help reducing it).
The temperature of the first bath is crucial. If your "cooldown time curve" is not repeatable you risk to have inconsistent developing results.
The first development of E-6, first one-shot use, lasts generally for 6:30 to 7:30 minutes, so your (only) problem is to device a system to keep the first bath chemistry near 38° for those few first minutes.
I don't know the Paterson Motorized Orbital tank. If it cannot be put in contact with warm water, maybe you can find a totally manual solution, keeping the tank in warm water and making manual inversion - agitation, more reliable. You obviously have to be very rigorous in your agitation - inversion pattern. I would also presoak film twice with water at treatment temperature to properly warm up film and tank as already advised in this forum.