The following are few possible solutions:
1) You could potentially use two Nano-10 PLC together to get 8 digital inputs, 8 digital outputs and 4 analog inputs. However, since you need 5 analog inputs it still will not fit unless you can multiplex the analog inputs (e.g. use the Nano-10 relay to multiplex two analog source to one analog input.
2) A single F1616-BA has 8 analog inputs, 16 digital inputs and 16 digital outputs (12 relays) and should fit your requirement.
3) Another solution is to use a Nano-10 as a master and a I-7018 thermocouple module and an E10-npn+ as slaves. I-7018 has 8 channels of thermocouple inputs, and E10 provides another 6 digital inputs and 4 digital outputs.
4) You could also use a Nano-10 as master (for webpage purpose since it has built-in Ethernet) and a T100MD88+ PLC as slave. T100MD888+ has 8 analog inputs, 8 digital inputs and 8 digital outputs and the combination provides more than enough I/O for your requirement.