As none answered my question, i will do so.
If you think that steam power was too far out of reach for the roman era, you might be surprised how close they came to it.
In order to explain that, i will have to delve into the reasons why England was able to develop a steam powered industry :
1 - Due to mercantilism, they had a large consummer market to feed and accumulated a lot of capital.
2 - The invention of water powered loom allowed large quantities of cloth to be produced to be sold on the asiatic markets.
3 - Their population was relatively small, they could not count on slave labour.
4 - They sided against slave labour because this would increase the potential market for their products in places like Latin America.
5 - The economical balance of Europe vis a vis Asia was favourable towards Asia, due to its large population and capacity to produce consequent of this.
This lead to a urgent need to increase productivity in England in order to balance out the commerce with asiatic countries. First they used water powered looms, but this was dependent on nearby source of water (rivers) with enough capacity to generate work. As the labour was not slaved, they had a somewhat bigger cost. This lead to the quick introduction of the steam power as soon as it was invented. The steam power was able to increase iron production, loom production etc, everything that the British sold abroad.
What the roman society lacked ?
1 - It was a slave labour society. All work was done by slaves.
2 - There was no need to increase productivity because the whole production chain was under roman autorithy, there was no competition. Romans solved competition via conquest. If Aegyptus had grain to feed Rome, conquering it was a solution, instead of competing with it.
But, there was a specific era during Roman empire where the influx of slaves decreased due to the decrease of Roman expansion. In some areas, there was already the use of water power to move machines.
This means that the Hero of Alexandria machine (an very early steam engine based on a reaction turbine) could very well be ressurected to provide power where it was not found.
So, with history in hindsight, we could very well see a steam powered "tank" in ancient era.
A big wood burning boiler is connected to a reaction turbine that spins quickly. This turbine is connected to a series of pulleys that turn rotation speed into torque. All the rotating elements are constantly lubricated by olive oil. This torque is applied into a bronze made chain that contacts the ground, moving the machine.
Over this "engine", a tower rises above ground 4 meters. On the top, a repeating ballista is placed and feed and aimed by a group soldiers.
The sheer ammount of firepower and aparrent invulnerability of the machine allows one to siege castles and break soldier formations. At the same time, the machine allows a good capacity to deal with horse archers from the asia.
A group of five of those machines is positioned in front of the infantry battle line. Cavalry protects the flanks, infantry comes behind the machine a la WW1.
The roman soldiers organize themselves as a traditional row and file of infantry armed with square shields and swords.
The machines advance. The romans try to bring archers to the front line in order to hit the soldiers manning the ballistas. But, as the machines get closer, a quick burst of arrows decimate roman archers who retreat behind the shield wall. The machines advance towards the cowering roman soldiers who break ranks and try to scape for their lives.
Now the accompanying infantry overtake the machines and attack the retreating deorganized roman soldiers.