So... one Arduino UNO can monitor 4 of the SHT15's and transmit the data wirelessly (thanks PaulS) via an XBee (of some sort) to a computer?
Yes.
Will the computer end of the transmission require another Arduino UNO, power supply (not through USB?), and XBee device(s)?
The PC end could consist of an XBee and a USB explorer (or there is a dongle version).
Is there a way for a solid state relay to operate something with higher voltage
That is the function of a relay, solid state or conventional.
All I need are an SHT15, XBee, power supply, and sensor wiring/casing at the tank, and with appropriate receiving equiptment (?? another XBee?) at the computer?
That is one way of doing it. It has advantages in that the sensor is close to the sender.
It has disadvantages in that the XBee has a smaller number of digital and analog pins, compared to an Arduino with XBee, and the XBee can't make decisions. The Arduino would be able to handle more inputs and make decisions, rather than the computer.
Anyone want to make one for me?
I'd be willing (PM me if interested). I have XBees and Arduinos and all the shields. The only things I don't have are the temperature/humidity sensor and solid state relay to control the fans/heaters.