Trying to replace a Bryant heat pump thermostat with 8 wires connected with a Honeywell RTH3100C. Instruction guide says if W1, W2, and Y were connected, contact a HVAC tech. Honeywell customer service was no help. Any ideas?

Post the color wires you have and we can tell you where to put them.

The old Bryant heat pump thermostat had 8 wires connected with no jumpers: G terminal(green wire), Y(yellow), E(brown), O(orange), W1(white), C(black), R(red), W2(blue). T and F terminals were empty.
Markings on the old Bryant thermostat are: BDP CO.P271-3453 with 3AAT83D14B2 below that.
The new Honeywell RTH3100C non-programmable digital thermostat has 9 terminals: E, Aux, Y, G, O, L, R, B, and C.

I am looking for a non programmable heat pump thermostat to replace my old energy saving bryant thermostat model No.34427DP97 installed in 1978.
The bryant thermostat uses 8 wires. It controls the heatpump and AC and automatically switches to propane gas when outdoor temperature drops to 32 degrees. It has an emergency heat switch and red indicator light for the propane gas also. Can you recommend a replacement?
Thank You