Important Note
Monty Wild pointed out to me in the comments below that this question is actually about terrestrial, hand-held weaponry. (I had thought it was about ship-to-ship space weaponry.) I will do a thorough edit of my answer a little later on, but in the meantime, I expect the main difference will be that the power source will be a limiting factor, and that friction and conductive heat losses in the atmosphere will further limit the weapon's effectiveness. Unless I think of something fairly major, the main takeaways will still be broadly the same.
Disclaimer: while all of this is based in real science, there are a few hypotheses here that I won't be able to test they let me up into orbit with my plasma cutter and tungsten forge.
It's hot. It's real hot.
The main issue will be temperature. Plasma is hot, like close to the surface of the sun hot. Plasma is created by heating a gas past $5\ 000^\circ \text{C}$. About your best bet for a metal container would be tungsten (W), which melts at around $3\ 400^\circ \text{C}$. As it turns out, the vacuum of space is a good insulator, so your only losses are going to be radiated visible and infrared (heat), so the tungsten will heat up.
The semi-good news is, tungsten doesn't boil until $5\ 930^\circ \text{C}$, and in the absence of other acceleration or strong gravitational fields, the tungsten and plasma will stay together in a spherical shape.
The bad news is, the plasma will exert considerable outward pressure (conventional and radiation pressure) on the tungsten vehicle, so it'll likely blow apart in fairly short order. If that doesn't happen, then because the liquid tungsten is far more dense than the superheated gas (plasma), it will "sink" to the center of the sphere as soon as there is any sort of surface irregularity in the tungsten.
Be quick about it.
The maybe good news is that heat transfer (be it via conduction, convection, or radiation) takes time, so if your plasma bolts are moving quickly enough and the target is close enough, they might survive. (This also assumes that they can be created quickly and fired instantly; no pre-loading, here!) This will limit the range and rate of fire of your weapon, obviously. Let's have a look at conduction. There, the heat transfer, $\text{Q}$ (in Joules), is given by:
$$Q = \frac{kA\Delta \text{T} t}{d}$$
$k$ is the object's thermal conductivity. Higher conductivity means your plasma bolt fizzles out more quickly.
$A$ is the cross sectional area between the hot and cold surfaces.
$\Delta \text{T}$ is the difference in temperature between hot and cold (in C or Kelvin; they're equivalent).
$d$ is the diameter of the material.
Thus, rearranging for $t$ (time):
$$t = \frac{dQ}{kA\Delta \text{T}}$$
As you can see, going with a larger bolt will mean it will take longer to transfer its heat, as will decreasing the surface area (a sphere is ideal). Getting exact values for some of these variables would take some more research, but you're probably reasonably safe with tens of seconds if your projectile is at least a few centimetres across. Hopefully that's enough time for a ship-to-ship impact.
Where does that leave us, then?
Plasma actually isn't all that amazing as a weapon. We already use it in plasma cutters today, and if you've ever seen a fabricator cut a piece of steel with a plasma torch, you'll know it takes a lot of sustained application of the plasma jet to melt and remove the material to make a 2mm-wide cut through even a 1cm piece of non-tempered ("soft") steel. That sort of hull breach could be plugged with bubble gum. Plasma, while very hot, is simply not dense enough to make much sense as a projectile payload with a more-or-less instantaneous impact. Everything that helps your projectile survive the travel time from your ship to theirs hurts its effectiveness at dumping all of its heat into the bad guys' hull. The tungsten container will do far more kinetic and thermal damage on impact than the plasma, unfortunately.
Even with advances in materials and science, this relationship isn't likely to change much, since the laws of thermodynamics are dominating the discussion at this point.
Is there an alternative?
At extremely close range (as in, you could reach out your airlock and write graffiti on their hull), a much larger version of a plasma torch might do some decent thermal damage, but its power falls off very quickly with distance.
Honestly, regular old kinetic projectiles (think: conventional guns) would be more effective. In the vacuum of space, friction won't slow them down, and if you're relatively far from massive celestial bodies, gravity won't bend their trajectory much. Also due to the lack of friction, with a very long barrel, you can accelerate the projectiles much much more than you could on Earth, without any additional energy input.
If you want some kind of energy weapon that does thermal damage, lasers are probably your best bet, unless you want to cross over into the realm of speculative/fantasy sci-fi to come up with your own version of phasers, photon torpedoes, etc., but that's clearly a different sort of question.