Towing

LL16 - Not a problem. The 7th Generation 2WD Hilux is rated at 2250kg, but the 4WD of the same model is rated at 2500kg towing capacity - and it's the same engine.

Toyota have had a few 3.0L Hilux piston failures, and have concluded it was caused by towing at highway speeds at maximum GCM - for long distances, continuously.

They have modified the pistons a couple of times, but apparently have still not eliminated piston cracking, under the same scenario of, "long distances, towing at maximum load, at highway speeds".

There have only been a small number of Hilux engines affected by the piston failure problem.
What caused more Hilux engine failures was the original, poor-quality injector seals, fitted between 2005 and 2007.
But the Hilux injectors should still be serviced every 100,000-120,000kms, regardless.

Hilux 7th Gen - recalls and known faults

Cheers, Ron.

It would depend on what you mean by pushing it the slow Lux doesn't exactly have a reputation of being a Powerhouse .
2ton poptop , is that it loaded weight or it labelled weight ? Plus how big a load are you likely to put in The Lux it self .
We toured with friends with a Lux and a camper
Van and 4 people and it definitely struggled passing , hills & headwinds...although was able to sit on the speed limit at times .

Lazylux16
Is your Hilux turboed?
If it is a manual Hilux to tow and used in too high a gear while towing, causes prolonged heat stress on the pistons which Ron mentioned above. You are better to allow the engine to spin a bit faster, ie, lower gear, rather than changing up and increasing the load on the engine. Lower engine loading reduces the exhaust gas temperature.
Matching the vehicle and it's abilities to the towed load is what is required.

LazyLux
I would fit an auto trans cooler if towing a heavy load. Having one in the exit/hot line from the auto gets rid of additional heat and DOES NOT add that heat developed by the torque converter to the engine coolant.
The engine will be working more and eveloping more heat into the coolant and so will the auto add to that, heaps of heat comes from the torque converter. If you want to keep auto temps respectably low and not tax the engone coolant system an auto cooler is a must. Imagine with the load up a hill on a hot day, with a tail wind with forward movent slower, is a situation which then makes the engine coolant system near to max or over the limit. All because of the additional heat from the auto which WILL be in slip mode and developing plenty of heat, heat which must be disipated to prevent overheating of both auto and engine.
Anyone who mentions you don't need one in your situation hasn't much of an understanding of mechanical systems, thermo dynamics or have little empathy for the vehicle.
PS
The harder working engine oil temp which will be higher than normal is cooled by the engine cooling system so it is working at elevated levels even without the auto fluid heat input into the coolant.

It also isnt recomended to tow in top gear in the auto especially if it is a 4 speed. I have a cooler and inline filter in mine which i change every 20 k, it does pick up some tiny shiny bits when back flushed with brake cleaner, and also run a full synthetic fluid. The transmissions apparently have too light an overdrive set up to handle heavy towing. Have a read in newhilux.net forum, several people have found out the expensive way. Towing about 1 ton of trailer and a well loaded ute in 3rd on dirt running 25psi all round also seen me adding a 145 litre arb tank, loves a drink but holds together.