In the mid 3050s, it was a good time to be the Free Worlds League. The FedCom had just gotten massively battered by the Clans and were buying all the war equipment you could price gouge them for, the proliferation of Star League tech meant that you were producing expensive upgrade kits for a lot of old mechs, and your economy and infrastructure hadn't been touched by any of the fighting. As such, the FWL began production of a flurry of new mechs. Enter the Tempest.
According to TRO 3055 (original), the Tempest actually began design in the 3040s before the Clan invasion. This configuration, dubbed the TMP-2M by the Master Unit List, was armed with two PPCs as its main weaponry but never entered production. Instead, the first variant produced was the TMP-3M, which was upgraded with a significant amount of Star League technology in its construction.
Powered by a 260XL engine, the 3M moves at a fairly typical top speed for an Inner Sphere heavy mech of 65 kph. Four jump jets provide supplemental mobility. This sets the standard for the Tempest's mobility, there isn't much variation on the 3M's 4/6/4 movement among the other configurations. Endo Steel for the chassis provides additional mass savings.
For protection, the TMP-3M mounts 12.5 tons of standard armor, providing it with near-max armor, arranged sensibly- it's short by three points in the Center Torso (32/7 for a total of 39 out of 42 points) and two points on each arm (18 out of 20 each) and leg (28/30). The arms fail the AC 20 check, which is a problem, but what can you do about it?
And that takes us to the armament. As stated before, originally the Tempest was to be armed with dual PPCs, but in the wake of the Clan Invasion its weapon loadout was changed. A Gauss Rifle with two tons of ammo resides in the Right Arm, while a large pulse laser sits in the left. Supplementing the big guns are a trio of medium lasers- two in the center torso and one in the head, and one SRM 6 pod in the left torso. Eleven double heat sinks is not sufficient to cool this mech's full loadout, but it's fairly easy to drop the large pulse laser any time you need to cool off. The mech's firepower is obviously biased toward infighting and its armor and jump jets let it perform pretty well at that range, though the XL engine makes it a bit vulnerable.
Well, that's the stock Tempest, but not the only one.
TRO 3055 Upgrade provides most of the variants, starting with the TMP-3G. A straightforward variant, this downgrades the SRM 6 to a 4-pod and uses the extra ton to add another eight shots to the Gauss Rifle. YMMV regarding whether or not this is useful. Certainly it's unlikely to matter in most pick up games.
The TMP-3MA is another straightforward variant, swapping the Gauss Rifle out for an AC 10 with four tons of ammo and also adding another double heatsink. It loses the mech's only long-range weapon, meaning that it probably wants to fight more in places where line-of-sight is more restricted, and of course it wants to take advantage of specialty ammo for the autocannon- you definitely don't want to walk into a fight packing 40 rounds of AC 10 ammo.
The TMP-3M2 "Storm Tempest" is the most radical variant so far, swapping the Gauss Rifle out for a Light Gauss Rifle with one ton of ammo- hey, it's a Marik mech, and upgrading the medium lasers to ER models and the SRM-6 to Streak. The extra heat sink from the 3MA shows up again, as does an ER small laser. The Storm Tempest also maxes out the armor.
After that, the Tempest didn't see any major changes until the Dark Age, when the TMP-4M debuted in TRO 3150's New Tech, New Upgrades section. Keeping the Gauss Rifle and the medium lasers from the 3M, the other weaponry was sacrificed for a Snub-nose PPC in the Left Arm and five Improved Jump Jets in the torsos, which necessitated moving the two medium lasers previous in the center torso to the right and left torsos. The armor is the same as the 3M's and it only mounts the stock 10 double heatsinks, but 20 dissipation is fine for it thanks to the reduced heat load from the loss of the SRM pod and the (slightly) reduced heat of the IJJs.
And the last variant, also from TRO 3150 is the only mixed-tech variant, the Tempest C. Again taking the stock 3M, it upgrades the Gauss Rifle and Large Pulse Laser to Clan configurations and uses the weight savings to swap out the SRM 6 for an ATM 9 fed by two tons of ammo. An extra heatsink doesn't quite keep up with the heat load, but it's only 2+movement on an alpha strike. The fluff in TRO 3150 suggests that the Wolf Empire was responsible for this upgrade, but the MUL only lists it as available to the FWL and Clan Protectorate, so sounds like something to ask in the MUL Errata section.
Edit: nckestrel has pointed out errata stating that it was actually the Sea Foxes, not the Wolves, who were responsible for the Tempest C upgrade. Thank you nckestrel.
Since I'm already editing this post: If Quirks are in play, the Tempest has one- Directional Torso Mount (Head Medium Laser). A minor quirk, but it does make attempting to flank the Tempest that much dangerous.
Overall, the Tempest is a solid and reliable design- the variants are all "the original but with one or two things changed", there's no radical shifts in performance or role for any of them. When I first saw it, I thought it looked an awful lot like it was derived from the Thunderbolt, though no official word says anything of the sort. But like the Thunderbolt it can dish out and take some damage and get the job done.