In that case, my reply to "What does it take to swap a Cummins 4BT into an H3" would be "Money. Plenty of money".
The first basic question is "Which engine"? The 4BT has been out of production for quite a few years, but good used engines and factory remans are readily available. The replacement for the 4BT is called the ISB3.9, and most recently the ISB4.5. Just as the 4BT is the 4 cylinder version of the 6BT (which is commonly called the "12V" or 12 valve Cummins in the Dodge world), the ISB3.9 and ISB4.5 are 4 cylinder versions of the electronically injected common-rail ISB5.9 and ISB6.7 respectively. The 6 cylinder ISB's (5.9L and 6.7L) used in Dodges are what are called "Front gear train" engines. That is, the gear train that drives the camshaft, injector pump, and accessory drive is located on the front of the engine. This keeps the rear part where the bellhousing adapter mounts more compact, making for a better/easier/possible fittting package in a pickup. By contrast, the medium duty and off-highway 5.9 and 6.7 ISB's, as well as ALL 3.9 and 4.5L 4 cylinder ISB's, are all rear gear train engines. This means the gear train for driving the cam, IP, and accessories are at the rear of the engine. The gear train cover has the SAE 2 or 3 bellhousing integrated with it. Not only does the rear gear train make the rear of the engine less fit-friendly in non-medium duty chassis, but the SAE housings exacerbate the fitment issues. The front gear trains are nice because you can put very compact flywheel housings (aka bellhousing/trans adapter) on the back, and the rear of the engine otherwise remains narrow and compact. The common Dodge adapters are quite compact, as are the adapters offered by
Destroked.
The whole point of that explanation is to point out that the newer ISB's would be a much more challenging fit than the older 4BT's. They're also more expensive, especially if injection systems components go bad. That said, they could be made to fit: here's a QSB4.5 (marine version of the ISB4.5 - same engine, different ratings) in a Jeep:
So far he claims to be getting 21.5MPG.
In contrast to the ISB's, the older mechanically injected 4BT's have been swapped into everything short of airplanes and go-karts. Part of the reason is size: Look how compact the engine is:
I seriously doubt that engine is longer than the H3's stock I5 - it may likely be shorter. The one above is the more desirable later version with the 7mm injectors and inline "P" pump. That engine with a set of larger injectors (~$400), a fuel plate (~$150), 3000RPM governor spring kit (~$100) and a timing bump (free) can do an easy 250HP and 500lb-ft of torque AT THE WHEELS.
Here's that same 4BT in the engine bay of a Toyota Tacoma:
So, yeah, it is physically doable. Motor mounts would need to be made, which is pretty basic stuff. IFS clearance could be an issue - until someone does a test fit there is no way to tell what, if anything, would need to be done. Most Cummins swaps into IFS vehicles are usually done concurrently with a solid axle swap. This doesn't necessarily have to be the case - often it is done simply because the swapper wants a stronger front end. Either way, different rate springs (or torsion bars) will be needed since the 4BT weighs about double what the I5 does, and about 250lbs or so more than the 5.3. With proper suspension mods the weight will not be noticeable in a rig as heavy as an H3.
Transmission is an issue. The 4L60E will do OK behind a stock 105-130HP 4BT, but I doubt the owner would be happy with that level of HP (although with the torque the engine makes they are surprisingly spry even at stock HP), and attaching it to the engine and controlling it will require the exact same parts as a 4L80E, so there is really no compelling reason to use it. The most popular automatic used in a 4BT swap is the Dodge 47RH, mainly because it is inexpensive, can be made very strong, easily adapts to the 4BT with stock Dodge parts, and doesn't need an aftermarket electronic controller. Next is probably the 48RE, which is electronically controlled and stronger in stock form, but otherwise a bolt-up. 3rd in popularity is the 4L80E, which requires a $1500 adapter kit to attach to the engine as well as a $600 controller to run it, but it keeps a GM trans in your rig. Also, being fully electronic, it is easier to program shift points and such vs a mechanical trans. Then there is the Allison 6 speed, which doesnt have a prayer of fitting in your trans tunnel without plenty of :hack:,:weld:, and :grind:. So, probably not an option. I should point out that trans options for the ISB 4's are more difficult since the engines only come with SAE adapters, so a custom SAE to trans-of-your-choice plate would have to be machined ($$$). The exception to this is the Allison, which has SAE bellhousings available (i am using a 6 speed Alliosn with an SAE #3 bellhousing in my swap), but like I said won't really fit in the H3 tunnel.
A change of transmission means a change of transfer cases. Depending on the trans used, whether you go SAS or not, whether you are willing to use a lever shifted case or demand electric shift, and the limit on your credit card will determine how painful or painless the t-case choice is.
Then there is electronics, or in the case of the 4BT, the lack thereof. Mechanically pumped engines only need 1 or 2 wires (depending on the pump) to run. Actually, if a mechanical shutoff is used they can run with NO electricity whatsoever. Throttle control on the 4BT is via a good ol' cable, just like in the stone ages
The ISB's have their ECM mounted to the engine, and generally require power, ground, throttle input, and perhaps one or two other minor doo-dads. Still pretty basic. The main issue may be the H3's other systems. At the very least the traction control is going to get pissed off since it does part of it's job by ordering torque reductions to the stock ECM, which is now gone. Probably the easiest solution to that issue is to eliminate the TCCM and hope the ABS module and BCM don't freak out too bad. that is where some more research would be needed, otherwise you might end up with constant alerts in your DIC display.
Finally, don't expect the 10b (aka 8.6") rear axle to be happy with your new-found torque. Plan on an axle upgrade during or shortly after the engine swap.
I think that covers all the major stuff. I will tell you from personal and second hand experience that engine swaps in general aren't cheap, and diesel swaps even less so. I have spent quite a bit on my Cummins swap and I am spending more still, but I have never looked back. Ask Todd (Crawler) what he spent on his 6.0L/4L80E swap. Still, if the vehicle is going to be a keeper and you don't mind the drawbacks of a diesel (mainly more noise - the ISB's are quieter, but no diesel will be as quiet as your I5), then it can be a very worthwhile and enjoyable swap. It mostly depends on you.