I design power stations (my wife sells the coffee) for a living - almost any PID controller will do the job. The difference in the outputs are this; most cheap PID controllers have a small relay (switch) as the output which is then used to drive a Solid State Relay (SSR) which is external to the machine. No problem with this the relay will last for millions of cycles providing it is driving a very small load like an SSR. Some more expensive PID's are fitted with a VERY small SSR output (sometimes called a transistor output) these will last indefinately, but you can blow them up very easily if you short circuit them. By the way - if you want cheap - then you can use a secondary mechanical power relay insted of an SSR, really the only difference is that you will hear the relay clicking in and out continously which is a bit annoying.
Almost any SSR will do, it does not matter if it is too big, it does matter if it is too small. RS components have a reasonable range. Pretty much all machine could be run from a 10A SSR, but 25A is OK, only difference is the price and the physical size. Cooling of SSR's should not be a problem as they are not switched on most of the time - even if you are drawing water/steam pretty continuously.
Last thing to consider is the PID parameters, most PID's have an autotune facility and you should try this first. If Autotune does not give the results you want (a nd it need time to learn so give it a chance) then adjust the P (proportional) control only until you get a fairly steady temperature - then you are likely to find that although the temperature is steady it is not what you ask for. This offset can be eliminated by increasing the I (Integral) control by a few seconds. Now you should have absolutely steady temperature and at the set point. BUT when you pull a shot the temperature will vary, so next (and this is often very tricky) set the D (Differential) control to repsond to rates of change of temperature. I expect you will need a very low setting for D otherwise the temperature will oscillate in a nice Sine wave. If in trouble do not use the D control at all and rely just on P & I.
Not sure how this would work on a heat exchange machine like the ISOMAC TEA I have and I think I will wait for the warranty to expire before I try!! But basically this is bound to be better than thermostat controls.
Anyone needing help setting up or wiring PID's I can help.
Ad.