“Trenbolone Cough” differs from user to user. Some have a high bloodflow in their buttcheeks, wich sometimes increases with prolonged AAS use. You’ll notice it if you bleed very often after an injection. I.m.o. those people are more predisposed to “tren cough” There are two different coughs, the notorious hard and uncontrolable one that starts right after or during injection and a milder controlable one that is just irritating. Some people claim that they taste a chemical, kinda methanol/solvent. If you pierce a vein or inject very close to a vein the trenbolone solution migrates up into your bloodstream and, within seconds the solution hit the lungs, the lungs react like you inhaled a toxin like b.e. smoke or an irritating chemical, and they try to expel it out by coughing. The problem is this is impossible because the irritation comes from the inside and leaves the body through the lungs/mouth.

Some users claim it is possible to surpress the cough by immmidiately start to inhale-exhale small amounts of air through the mouth, like you’re hyperventilating or like women do to surpress the contractions during labour. Some also claim that the short estered acetate is more irritating then the longer estered enanthate or hydrohexacarbenzylcarbonate (parabolan) the last one also gives a kinda metallic taste in the mouth immidiatly after injection.

Personally I believe it’s the trenbolone molecule (wich differs from most steroid molecules) causes the irritation in the lungs, not the solvents like benzyl alcohol or benzyl benzoate as many believe. The solvents are present in other injectable steroids and nobody complaints about heavy coughing with those compounds.

I’ve read an interesting theory ( i don't agree with it by the way 8) ) about the tren cough and the fat burning capacity wich caused Trenbolone to be nicked as “the poor mans growth hormone”:

Tren- Fat burning and "Tren cough" both from prostaglandin metabolization by pheedo

It's been widely disussed of Trens fat burning properties through rises in IGF and Prostaglandins. While IGF is a fairly well known substance in the bodybuilding world today, prostaglandins are fairly unknown in terms of formation and roles in the body.
So below, a brief dicription of prostoglandins and their role in fat burning, "fina cough", and why a person going through Tren administration can experience it's fat burning effects without the dreaded "Cough"

The term prostaglandin comes from the word-Prostate. The first prostoglandins were first dicovered in semen about the mid 1930's and it was thought that prostaglandins were made from the prostate. Since this time, it has been dicovered that most prostaglandins are not even constructed in the prostate.

Prostaglandins are made by two different pathways(Cyclooxygenase and Lipoxygenase), and considering prostaglandins are a group of about 20 lipid cells, they have contrary function; responsible for stimulating as well as alleviating inflammation(Inflammation stimulation is the rapid metabolism of them expelled through the bronchials), regulate blood flow to particular organs, control ion transport across membranes, modulate synaptic transmission, induce sleep, mediate lipid release, and regulate metabolism is various tissue.

Prostaglandins are synthesized from arachidonate(Lipoxygenase which catalyze the dioxygenation of polyunsaturated fatty acids) in the cell membrane by the action of phospholipase A2. Cyclooxygenase and lipoxygenase pathways, compete with one another to form prostaglandins(as well as thromboxane or leukotriene-leukotriene being a bronchial stimulator),
In the cyclooxygenase pathway, the prostaglandins D, E and F plus thromboxane and prostacyclin are made. Thromboxanes are made in platelets and cause constriction of vascular smooth muscle and platelet aggregation
Leukotrienes are made in leukocytes and macrophages via the lipoxygenase pathway. They are potent constrictors of the bronchial airways. They are also important in inflammation and hypersensitivity reactions as they increase vascular permeability.

Being that prostaglandins from either pathway, are still fatty acids of a group, they mediate lipid release and controll tissue metabolization, so fat burning is a luxerry of either pathway of formation. It's the pathway from which they are constructed that dictates "fina cough". As prostaglandins made from the Cyclooxygenase pathway dictate muscle constriction and platlet aggregation, and the Lipoxygenase pathway dictates bronchial constriction(the main form of expulsion)

Refs:
Cackatoo Press
Columbia Encyclopedia 6th Edition
Science Daily Magazine