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small chiller/heater for radiant bed
$700 is not a lot, so this is what I would do:
Buy a small electric hot water heater (1500 W point of use type), with an expansion tank, circulator and fittings. You can get all this for about $300. (Heater is about $150, circulator about $80, expansion tank -Watts #5- runs about $25, plus valves and fittings.)
Set up your Pex-Al-Pex or regular O2-barrier PEX as you need to (too much to get into here). If you can get your heater with a rheostat variable controller, even better.
That is your heat.
Cooling in my estimation is not possible using machinery in that price range. (If money were no option, a nice Filtrene unit at $6,000 would be ideal :)
For cooling, I would use the same heater/hydronic setup but instead of using the heating element, bleed in/drain off domestic water to maintain temperature. A good thermostatic bulb valve can maintain temperature. Key to me would be to keep the water "cool not cold" above the room dewpoint to avoid sweating. Provided of course that this meets your temperature criteria where it counts.
This will waste water, but the trade-off is unaffordable first cost and energy cost associated with that.